I did some research, and this is what I understood about. I tried to put it in a way for easy understanding, thats why it looks brief and short.

FATHER ("Insight on the Scriptures" Volume 1, pages 814-815)

The Hebrew word ’av, translated “father,” is a mimetic (imitative) word taken from the first and simplest sounds of infant lips. The Hebrew ’av and the Greek pa·ter´ are both used in various senses: as begetter, or progenitor, of an individual (Pr 23:22; Zec 13:3; Lu 1:67), the head of a household or ancestral family (Ge 24:40; Ex 6:14), an ancestor (Ge 28:13; Joh 8:53), a founder of a nation (Mt 3:9), a founder of a class or profession (Ge 4:20, 21), a protector (Job 29:16; Ps 68:5), the source of something (Job 38:28), and a term of respect (2Ki 5:13; Ac 7:2).

YHWH God as Creator is called Father. (Isa 64:8; compare Ac 17:28, 29.) He is also the Father of spirit-begotten Christians, the Aramaic term ’Ab·ba’´ being used as an expression of respect and of close filial relationship. (Ro 8:15.) All who express faith with a hope of everlasting life can address God as Father. (Mt 6:9) Jesus Christ, the Messiah, because of being God’s Chief Agent of life, was prophetically called Eternal Father. (Isa 9:6) Also, anyone who has imitators and followers, or those who exhibit his qualities, is regarded as a father to them. (Mt 5:44, 45; Ro 4:11, 12) In this sense the Devil is spoken of as a father.—Joh 8:44; compare Ge 3:15.

Applying “father” to men as a formalistic or religious title was forbidden by Jesus (Mt 23:9). Because of Paul’s bringing the good news to certain Christians and nourishing them spiritually he was like a father to them, but in no scripture is “father” applied to him as a religious title. (1Co 4:14, 15) Paul likened himself to both a father and a mother in his relation to the Thessalonian Christians. (1Th 2:7, 11) Whereas reference is made at Luke 16:24, 30 to “father Abraham,” this is basically in the sense of fleshly ancestry.

SPIRIT ("Reasoning from the Scriptures", pages 380-384)

Definition: The Hebrew word ru´ach and the Greek pneu´ma, which are often translated “spirit”, have a number of meanings. All of them refer to that which is invisible to human sight and which gives evidence of force in motion. The Hebrew and Greek words are used with reference to (1) wind, (2) the active life-force in earthly creatures, (3) the impelling force that issues from a person’s figurative heart and that causes him to say and do things in a certain way, (4) inspired utterances originating with an invisible source, (5) spirit persons, and (6) God’s active force, or holy spirit. Several of these usages are here discussed in relation to topics that may arise in the field ministry.

What is the holy spirit?

A comparison of Bible texts that refer to the holy spirit shows that it is spoken of as ‘filling’ people; they can be ‘baptized’ with it; and they can be “anointed” with it. (Luke 1:41; Matt. 3:11; Acts 10:38) None of these expressions would be appropriate if the holy spirit were a person. Jesus also referred to the holy spirit as a “helper” (Greek, pa·ra´kle·tos), and he said that this helper would “teach,” “bear witness,” “speak,” and ‘hear.’ (John 14:16, 17, 26; 15:26; 16:13) It is not unusual in the Scriptures for something to be personified. For example, wisdom is said to have “children”. (Luke 7:35) Sin and death are spoken of as being kings. (Rom. 5:14, 21) While some texts say that the spirit “spoke,” other passages make clear that this was done through angels or humans. (Acts 4:24, 25; 28:25; Matt. 10:19, 20; compare Acts 20:23 with 21:10, 11.) At 1 John 5:6-8, not only the spirit but also “the water and the blood” are said to ‘bear witness’. So, none of the expressions found in these texts in themselves prove that the holy spirit is a person.

The correct identification of the holy spirit must fit all the scriptures that refer to that spirit. With this viewpoint, it is logical to conclude that the holy spirit is the active force of God. It is not a person but is a powerful force that God causes to emanate from himself to accomplish his holy will.—Ps. 104:30; 2 Pet. 1:21; Acts 4:31.

Hope this would answer your question... ;)

These 2 books I used is released by "Watchtower Bible and Track Society" in 1985/1989. In these books there are mentioned their web page, witch is actually looks like it's closed, and is guiding to visit JW.org. This is where I found that they have many of their publications available to download in e-pub or PDF formats, but I couldn't see the books I used to quoted from.

In some ways the best way to observe the different relations that exist within trinity is in how they operate in their unified works. It is well described by John Owen:

The beginning of divine operations is assigned unto the Father, as he is fons et origo Deitatis,—“the fountain of the Deity itself:” “Of him, and through him, and to him, are all things,” Rom. 11:36. The subsisting, establishing, and “upholding of all things,” is ascribed unto the Son: “He is before all things, and by him all things consist,” Col. 1:17. As he made all things with the Father, so he gives them a consistency, a permanency, in a peculiar manner, as he is the power and wisdom of the Father. He “upholdeth all things by the word of his power,” Heb. 1:3. And the finishing and perfecting of all these works is ascribed to the Holy Spirit, as we shall see. (Works of John Owen, Vol 3, P94)

We can see these relations in the very first three verses of the Bible:

In the beginning God created the heavens and the earth. Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters. And God said, “Let there be light,” and there was light. (Genesis 1:1-3, NIV)

We see that God the Father is the originating will being expressed through the Son, for 'God says' that is the Father expresses the Son who is his word in creating and sustaining the creation. The Son proceeds from the Father. Regarding the Spirit, he is said to be sent from the Father and sent from the Son. In this example right from the beginning, the earth is formless but the Spirit is hovering over the waters. This establishes a concept that the Holy Spirit is about to add a perfecting completion of the Trinity's work, finishing the creation into perfection after originated in the Father's command through his word, the Son. The Spirit is acting as the perfecting and immediate cause of the operations of the Godhead in and on the creation. The relation therefore of the Holy Spirit to the Father, is that the Holy Spirit 'proceeds' from the Father, being his immediate presence to his creation and perfecting the works of the Godhead which originally proceed from the Father. The Spirit never sends the Father anywhere. This seems to the key distinction in the Spirit's relation to the Father. It might seem like a minor point, yet it established a clear relation.

The Father, Son and Spirit are 3 separate persons. The Father is not the Son or the Spirit and vice-versa. (eg It was not the father Who died on the cross and it was the Spirit Who came upon the disciples at Pentecost.)

All 3 Persons are equal in power and glory. There is no distinction at all on that point. That is because they all fully partake of the essence of what it means to be God (Eternal & unchangeable in His being, wisdom, power, holiness, justice, goodness and truth....Summary only). The one essence is not the persons though. I think of essence more as characteristics, though the characteristics must be combined in to an indissoluble whole to comprise the essence of what it means to be God.

So there is no hierarchy of power between the 3 Persons. There is only differentiation of roles. eg the Father elects, the Son pays the price of redemption and the Holy Spirit applies to us the redemption purchased by the Son.

1Jn 5:7 For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one.

Mat 28:19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:

Act 10:38 How God anointed Jesus of Nazareth with the Holy Ghost and with power: who went about doing good, and healing all that were oppressed of the devil; for God was with him.

Let me introduce you to God as described in the New Testament by Jesus through John and Paul. So to start briefly with 1st John 5 and Acts 10. In John 5 we see the Father, Jesus and the Holy Spirit all called God or those which bear record in heaven and they are called three are one in the same sentence. No man accurately understands what that means and that's ok.

Joh 14:9 Jesus saith unto him, Have I been so long time with you, and yet hast thou not known me, Philip? he that hath seen me hath seen the Father; and how sayest thou then, Shew us the Father? Joh 14:10 Believest thou not that I am in the Father, and the Father in me? the words that I speak unto you I speak not of myself: but the Father that dwelleth in me, he doeth the works. Joh 14:11 Believe me that I am in the Father, and the Father in me: or else believe me for the very works' sake.

The Father is God and one with Christ Jesus and worked through Christ on the Earth. The Father is revealed to us throughout the Old Testament using many different Names which reveal attributes of His personality. This is an edited version of the links semi-exhaustive study on the names of God focusing on those which had a clear translatable meaning.

1. Elohim (Mighty Ones) 2606x Genesis 1:1
2. El (Might, Power) 245x Genesis 14:18
3. Eloah (Mighty One) 57x Nehemiah 9:17
4. Adon (Lord, Ruler) 335x Joshua 3:11
5. Adonai (Lords, Rulers) 434x Genesis 15:2
6. El-Elyon (Supreme Might) Genesis 14:18
7. El-Shaddai (Might of the Powerful Ones) Genesis 17:1
8. Cela (craig) Tzur (rock or strength) Ps 18:2 (used interchangeably)
9. YHWH-sabaoth (Lord of Armies) 285x 1 Samuel 1:3
10. YHWH-jireh: will see or provide Genesis 22:14 
11. YHWH-rapha: heals Exodus 15:26 
12. YHWH-nissi: our banner or victory Exodus 17:15 
13. YHWH-m'kaddesh: sanctifies Exodus 31:13
14. YHWH-shalom: peace Judges 6:24 
15. YHWH-raah: my shepherd Psalm 23:1 
16. YHWH-hoseenu: creator Psalm 95:6 
17. YHWH-tsidkenu: righteousness Jeremiah 23:6 
18. YHWH-shammah: Present and available when 

Any of these words can describe God the Father, Son or the Holy Spirit however lets assume the focus of the revelation in the Old Testament was on the Father and these words are used with preference to describe Him.

Psa 139:7 Whither shall I go from thy spirit? or whither shall I flee from thy presence? Psa 139:8 If I ascend up into heaven, thou art there: if I make my bed in hell, behold, thou art there. Psa 139:9 If I take the wings of the morning, and dwell in the uttermost parts of the sea; Psa 139:10 Even there shall thy hand lead me, and thy right hand shall hold me. Psa 139:11 If I say, Surely the darkness shall cover me; even the night shall be light about me. Psa 139:12 Yea, the darkness hideth not from thee; but the night shineth as the day: the darkness and the light are both alike to thee.

Heb 6:18 That by two immutable things, in which it was impossible for God to lie, we might have a strong consolation, who have fled for refuge to lay hold upon the hope set before us:

Again the following attributes apply to God the Father, God the Son before and after His earth ministry (Php 2:8) and God the Holy Spirit. God is omnipresent as Psalms 139 goes into great lengths to describe. We also know God is not omnipotent as he cannot lie and cannot do evil like temptation (James 1:13) or be afraid (1 John 4:18). The Lord God is omniscient (Psalm 147:5,1Jn 3:20,Psalm 147:5).

John 14-16 is the dissertation on the Holy Spirit. Here Christ describes the Holy Spirit in clarity which is not seen again till the Pauline epistles. I don't pray to the Holy Spirit because in the farewell sermon Jesus never mentioned us expressly praying to the Holy Spirit. I do not condemn you if you do.

Mat 6:9 After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name.

Joh 14:16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever;

Superficially the first thing one would notice about the difference between the Father and the Holy Spirit is: The Father's primary residence is in Heaven; The Holy Spirit's primary residence is on Earth. They are however both everywhere.

Joh 17:16 They are not of the world, even as I am not of the world. Joh 17:17 Sanctify them through thy truth: thy word is truth.

Joh 14:17 Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.

Eph 3:16 That he would grant you, according to the riches of his glory, to be strengthened with might by his Spirit in the inner man; Eph 3:17 That Christ may dwell in your hearts by faith; that ye, being rooted and grounded in love,

1Jn 3:9 Whosoever is born of God doth not commit sin; for his seed remaineth in him: and he cannot sin, because he is born of God. 1Jn 3:10 In this the children of God are manifest, and the children of the devil: whosoever doeth not righteousness is not of God, neither he that loveth not his brother.

God's Word Jesus Himself is truth. The Holy Spirit is not the Word which is truth He is the Spirit of truth. Christ and His Spirit dwell in our Hearts according to the scripture. According to 1st John 3:10 God the Father's seed is in us.

Joh 15:26 But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me:

G1607 ἐκπορεύομαι ekporeuomai ek-por-yoo'-om-ahee

From G1537 and G4198; to depart, be discharged, proceed, project: - come (forth, out of), depart, go (forth, out), issue, proceed (out of).

The Holy Spirit proceed from the Father. The word proceed has many sub words in Strong's Greek dictionary number G1607. Each of them describe the action of the Holy Spirit beginning His work on the earth.

Joh 16:7 Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you.

What we experience with the Holy Spirit is better than having Jesus who was and is one with God the Father present with us on the earth today. It is unknown exactly why Christ is at the right hand of Majesty on High and the Holy Spirit was sent here. The Holy Spirit is very kool to be able to fill the void of Christ in a better way than Christ Himself. So here we notice the Holy Spirit is better for us than Christ physical presence on the Earth.

Joh 16:8 And when he is come, he will reprove the world of sin, and of righteousness, and of judgment: Joh 16:9 Of sin, because they believe not on me; Joh 16:10 Of righteousness, because I go to my Father, and ye see me no more; Joh 16:11 Of judgment, because the prince of this world is judged.

Joh 3:19 And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil.

The primary work of the Holy Spirit on those in the world is to reprove or you could say convict of sin, righteousness and judgement. To be convicted means to be pronounced guilty. It is often thought that the Holy Spirit condemns people to hell or bring condemnation but that is an act of the individuals heart caused by the law.

Joh 16:12 I have yet many things to say unto you, but ye cannot bear them now. Joh 16:13 Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come. Joh 16:14 He shall glorify me: for he shall receive of mine, and shall shew it unto you. Joh 16:15 All things that the Father hath are mine: therefore said I, that he shall take of mine, and shall shew it unto you.

Here is a very high density amount of the word he. However it is important to note that the Greek word translated he here really is gender neutral however the word translated Comforter is indeed masculine.

The Holy Spirits work in the Church today is to complete the scripture in the lives of the believers. The primary way He did this was through the apostles, Luke and Mark writings after He arrived on the Earth. However He guides us into all truth not just those expressly written in the Word. He is able to enlighten the eyes of our understanding so that we know. He does not speak of Himself which is why we only know Him through the writings in the word and what we have experienced of Him. He does not speak from his omniscience. He speaks what he hears the implication is what he hears through your ears. The Holy Spirit also primary function in the Church today is revelation while in rare situations this can mean visions and dreams the majority of the way people experience God is through supernatural knowings one of the manifestations of the spirit. This is not hearing voices but experiencing the enlightenment from the scripture for your situation. Again Jesus says that the Holy Spirit is glorifying Christ and revealing the nature of Christ in and to us.

1Co 12:4 Now there are diversities of gifts, but the same Spirit. 1Co 12:5 And there are differences of administrations, but the same Lord. 1Co 12:6 And there are diversities of operations, but it is the same God which worketh all in all.

Again we see the Father, Son and the Holy Spirit in unison benefiting of the Church. God the Father is said to work all in all and to head the operations. God the Son administers and God the Holy Spirit is the Spirit behind the endowments.

1Co 12:7 But the manifestation of the Spirit is given to every man to profit withal.

Every instance of the endowments is a manifestation of the Holy Spirit, administered by Christ and worked by God the Father's Power. I follow the Pentecostal pioneer Howard Carter division of the Holy Spirits manifestations which I will briefly relate bellow. He divides them into three manifestations which know something, three manifestations which do something and three manifestations which say something.

1Co 12:8 For to one is given by the Spirit the word of wisdom; to another the word of knowledge by the same Spirit;

Word of wisdom is a knowing about the future. Like if you knew you shouldn't go to work on 9/11. This is not fortune telling it is just a word a single element conveying understanding about a situation. It is not a paragraph or a book. Likewise work of knowledge is a single element conveying present or past tense knowledge about a situation. Combined with discerning of spirits these are the three gifts which know something.

1Co 12:9 To another faith by the same Spirit; to another the gifts of healing by the same Spirit;

The gift of faith is often called special faith as it is what is necessary to receive that which is beyond what a person may normally believe for on their own. Gifts of healing is plural. This is not going to a doctor but God working with the doctor to heal your aliment of body or mind. Spirits are not healed in the New Testament they are saved.

1Co 12:10 To another the working of miracles; to another prophecy; to another discerning of spirits; to another divers kinds of tongues; to another the interpretation of tongues:

The working of miracles are miraculous healings (like arms growing back) and other wonders (like supernatural provision or walking on water) which defy nature. Special faith, healing and miracles are the three gifts which do something.

Discerning of spirits is disliked because many people who claim to see spirits or hear spirits are in fact are sick and need help from doctors. However that does not change that the Holy Spirit sometimes chooses to reveal a spirit to a person. The good sense you cannot explain when you go to church is a right example of discerning of spirits.

1Co 12:11 But all these worketh that one and the selfsame Spirit, dividing to every man severally as he will.

Every time one of these manifestations is rightly expressed the Holy Spirit is rightly getting His will and work accomplished in the earth.

Gal 5:22 But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith, Gal 5:23 Meekness, temperance: against such there is no law. Gal 5:24 And they that are Christ's have crucified the flesh with the affections and lusts.

Finally because everything is cross referenced in the word. We are able to discern whether what someone calls the manifestation of the Holy Spirit is in fact a manifestation of the Holy Spirit based on the attributes of the Spirit Himself as described in Galatians 5. If it does not meet the criteria of these verses people are just imagining that the Holy Spirit is manifesting Himself.

So in summery to differentiate the Father from the Holy Spirit you take all the things which are known to be directly attributed to the Father and all the things which are directly attributed to the Holy Spirit and you compare and contrast them. I briefly gave you several names of God describing his personality and several names of the Holy Spirit. Then I described the Holy Spirit manifestation's in the earth which the Father works. Finally I list the attributes of the Holy Spirit at work in the individual believers life to give you an idea of what a believer should show evidence of when inspired by the Holy Spirit directly.