Jesus' Soul and Spirit?

The three are three separate persons with separate emotions and wills, but they are in one accord and unity. This is why at baptism of Jesus we see Jesus baptized, Holy Spirit coming upon him, and the Father speaking from heaven.

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

The soul contains mind, will, and emotions.

When we are saved it is our spirit made alive, we are no longer spiritually dead so we can join a fellowship with God.

Our souls must still be sanctified by knowing and obeying the word of God.

1. Salvation starts with our spirit.
2. The soul must still be continually sanctified.
3. The body is healed by the beatings Jesus suffered and one day we will have glorified bodies if we conquer sin by the Spirit of God.

Humans are said to have body, soul, and spirit--all three. Because Jesus was human like us, he also had these three. However, in addition to these, Jesus also had the indwelling presence of God's spirit, which the Bible calls "all the fulness of the Godhead" (see Colossians 2:9), and, as noted in the question, God is spirit (see John 4:24). This means when we speak of Jesus' spirit, we need to be careful to clarify whether we refer to God's indwelling presence, or to his human spirit.

Here are Bible passages that address these points.

The soul and the spirit are paralleled

With my soul have I desired thee in the night; yea, with my spirit within me will I seek thee early: for when thy judgments are in the earth, the inhabitants of the world will learn righteousness. (Isaiah 26:9, KJV)

Humans have a spirit

And in the second year of the reign of Nebuchadnezzar Nebuchadnezzar dreamed dreams, wherewith his spirit was troubled, and his sleep brake from him. (Daniel 2:1, KJV)

For if I pray in an unknown tongue, my spirit prayeth, but my understanding is unfruitful. (1 Corinthians 14:14, KJV)

And they stoned Stephen, calling upon God, and saying, Lord Jesus, receive my spirit. (Acts 7:59, KJV)

Jesus also has a spirit

And immediately when Jesus perceived in his spirit that they so reasoned within themselves, he said unto them, Why reason ye these things in your hearts? (Mark 2:8, KJV)

In that hour Jesus rejoiced in spirit, and said, I thank thee, O Father, Lord of heaven and earth, that thou hast hid these things from the wise and prudent, and hast revealed them unto babes: even so, Father; for so it seemed good in thy sight. (Luke 10:21, KJV)

And when Jesus had cried with a loud voice, he said, Father, into thy hands I commend my spirit: and having said thus, he gave up the ghost. (Luke 23:46, KJV)

Yet Jesus has The Holy Spirit

And Jesus being full of the Holy Ghost returned from Jordan, and was led by the Spirit into the wilderness, (Luke 4:1, KJV)

And Jesus returned in the power of the Spirit into Galilee: and there went out a fame of him through all the region round about. (Luke 4:14, KJV)

Conclusion

The Bible teaches that Jesus has both a human spirit, just as we do, and he has the indwelling Spirit of God, the Holy Spirit. No mention is made in the Bible of Jesus' soul; therefore, this answer necessarily lacks support to directly address that aspect of the question.

"soul" and "spirit" are very different things, and it's impossible to understand Christianity without understanding that difference.

Soul

Souls are simply living bodies, both human and animal:

And God said, Let the earth bring forth the living creature [nephesh = soul] after his kind, cattle, and creeping thing, and beast of the earth after his kind: and it was so.
— Genesis 1:24

And to every beast of the earth, and to every fowl of the air, and to every thing that creepeth upon the earth, wherein there is life [nephesh = soul] …
— Genesis 1:30

This is the law of the beasts, and of the fowl, and of every living creature [nephesh = soul] that moveth in the waters, and of every creature [nephesh = soul] that creepeth upon the earth
— Leviticus 11:46

People don't have souls, they are souls:

… and man became a living soul [nephesh].
— Genesis 2:7

Souls aren't immortal; they can die:

… the soul [nephesh] that sinneth, it shall die
— Ezekiel 18:4

Whosoever toucheth the dead body [nephesh = soul] of any man …
— Numbers 19:13

And he that killeth any man [nephesh = soul] shall surely be put to death. And he that killeth a beast shall make it good; beast [nephesh = soul] for beast [nephesh = soul].
— Leviticus 24:17,18

Spirit

Spirit is an immaterial supernatural substance or energy that exists in various forms and serves various purposes.

All living souls have spirit that animates them:

And they went in unto Noah into the ark, two and two of all flesh, wherein is the breath [ruach = spirit] of life.
— Genesis 7:15

Unlike the animals, humans also have spirit that gives them consciousness and understanding:

But there is a spirit [ruach] in man: and the inspiration of the Almighty giveth them understanding.
— Job 32:8

Some humans are given a gift of additional spirit:

And thou shalt speak unto all that are wise hearted, whom I have filled with the spirit of wisdom …
— Exodus 28:3

Jesus's sacrifice enabled mankind to receive a different kind of spirit, the ultimate gift in which part of God's own spirit is given to man.

For by one spirit are we all baptized into one body …
— 1 Corinthians 12:13

After a Christian has received God's spirit by the laying on of hands, it becomes part of that person and can be seen as their character. It becomes their duty to develop a perfect character:

Be ye therefore perfect, even as your Father which is in heaven is perfect.
— Matthew 5:48

The disciple is not above his master: but every one that is perfect shall be as his master.
— Luke 6:40

And the glory which thou gavest me I have given them; that they may be one, even as we are one: I in them, and thou in me, that they may be made perfect in one; and that the world may know that thou hast sent me, and hast loved them, as thou hast loved me.
— John 17:22,23

Finally those pre-nascent spirits will be reborn with the gift of immortality:

Now this I say, brethren, that flesh and blood cannot inherit the kingdom of God; neither doth corruption inherit incorruption. Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed, In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed. For this corruptible must put on incorruption, and this mortal must put on immortality. So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory.
— 1 Corinthians 15:50–54

Seeing ye have purified your souls in obeying the truth through the spirit unto unfeigned love of the brethren, see that ye love one another with a pure heart fervently: Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever.
— 1 Peter 1:22,23

There is of course also holy spirit that God uses to communicate and interact with the physical world.

Jesus

In order to provide salvation to mankind, Jesus was born as a human being, without any divine nature:

Let this mind be in you, which was also in Christ Jesus: Who, being in the form of God, thought it not robbery to be equal with God: But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men: And being found in fashion as a man, he humbled himself, and became obedient unto death, even the death of the cross.
— Philippians 2:5–8

The NLT version makes his humanness more explicit:

… he took the humble position of a slave and was born as a human being.

Jesus was a fully mortal human being. (Remember, he didn't have a soul, he was a soul.) He was like us in every way except one: he was born already having the spirit of perfect character, the same spirit of character that humans can receive. He was able to communicate with God through his holy spirit. He was able to perform miracles, not as a human being and certainly not as a god, but by allowing God's spirit to work through him.

Following baptism and receiving God's holy spirit at the Pentecost meeting, many of his disciples were also able to use God's holy spirit to perform miracles and to communicate with God. But they, just like Jesus, were still fully mortal human beings.

Three days after his death, Jesus was resurrected from the dead and his spirit became immortal, just as those human beings that have accepted salvation during this age will be reborn as immortal spirits at Jesus's return.

Jesus' Soul and Spirit?

Man is made up of both soul and body. Together these make man a human being. Jesus, as the Second person of the Trinity, in his humanity was composed of both body and soul. Sometimes, both Scriptures and people refer to the soul of an individual as his spirit!

Here follows a what the Catholic Encyclopedia has to say about the word spirit:

(Latin spiritus, spirare, "to breathe"; Gk. pneuma; Fr. esprit; Ger. Geist). As these names show, the principle of life was often represented under the figure of a breath of air. The breath is the most obvious symptom of life, its cessation the invariable mark of death; invisible and impalpable, it stands for the unseen mysterious force behind the vital processes. Accordingly we find the word "spirit" used in several different but allied senses: (1) as signifying a living, intelligent, incorporeal being, such as the soul; (2) as the fiery essence or breath (the Stoic pneuma) which was supposed to be the universal vital force; (3) as signifying some refined form of bodily substance, a fluid believed to act as a medium between mind and the grosser matter of the body. The hypothesis of "spirits" in this sense was familiar to the Scholastic age, in fact down to the end of the eighteenth century, "animal spirits", "vital spirits", "natural spirits" were acknowledged agencies in all physiological phenomena (cf. Vesalius, Descartes, Harvey, Erasmus, Darwin, etc.) "Magnetic" spirits were employed by Mesmer in his theory in very much the same way as modern Spiritists invoke the "ether" of the physicists.

In Psychology, "spirit" is used (with the adjective "spiritual") to denote all that belongs to our higher life of reason, art, morality, and religion as contrasted with the life of mere sense-perception and passion. The latter is intrinsically dependent on matter and conditioned by its laws; the former is characterized by freedom or the power of self-determination; "spirit" in this sense is essentially personal. Hegelianism, indeed, in its doctrines of Subjective, Objective, and Absolute Spirit, tries to maintain the categories of spiritual philosophy (freedom, self-consciousness and the like), in a Monistic framework. But such conceptions demand the recognition of individual personality as an ultimate fact.

In Theology, the uses of the word are various. In the New Testament, it signifies sometimes the soul of man (generally its highest part, e.g., "the spirit is willing"), sometimes the supernatural action of God in man, sometimes the Holy Ghost ("the Spirit of Truth Whom the world cannot receive"). The use of this term to signify the supernatural life of grace is the explanation of St. Paul's language about the spiritual and the carnal man and his enumeration of the three elements, spirit, soul, and body, which gave occasion to the error of the Trichotomists (1 Thessalonians 5:23, Ephesians 4:23).

Matter has generally been conceived as in one sense or another the limitation of spirit. Hence, finite spirits were thought to require a body as a principle of individuation and limitation; only God, the Infinite Spirit, was free from all admixture of matter. Thus, when we find the angels described as asomatoi or auloi, in the writings of the Fathers, this properly means only that the angels do not possess a gross, fleshly body; it does not at all imply a nature absolutely immaterial. Such Scripture expressions as "bread of angels", "they shall shine as the angels", as well as the apparitions of these heavenly beings, were adduced as proofs of their corporeality. So speak Sts. Ambrose, Chrysostom, Jerome, Hilary, Origen and many other Fathers. Even in Scholastic times, the degree of immateriality that belongs to finite spirits was disputed. St. Thomas teaches the complete simplicity of all spiritual natures, but the Scotists, by means of their famous materia primo prima, introduced a real composition, which they conceived to be necessary to a created nature. As regards the functions of spirits in the world, and their active relations to the visible order of things. Scripture abounds in instances of their dealings with men, chiefly in the character of intermediaries between God and His servants. They are the heralds who announce his commands, and often too the ministers who execute His justice. They take a benevolent interest in the spiritual good of men (Luke 15:10). For these reasons, the Church permits and encourages devotion to the angels.

This matter has been debated over the centuries because it is very important with regard to the biblical gospel message of Christ Jesus - his nature, and the way he could be both divine and human. Who is this Jesus? How could a man achieve what the Bible says he achieved and be "the one Mediator between God and men, the man Christ Jesus" (1 Timothy 2:5)? The doctrine that deals with this is spoken of as "the hypostatic union" and it has a long history.

With regard to this, it was proposed and developed because some realised that the truth of the gospel was at stake. Although it is generally accepted as orthodox (even if poorly understood by many) the unbiblical ideas that gave rise to the debates of old are still alive today, even in some branches of Christianity that claim to accept it. So, this is an important question to raise.

In a nutshell, the doctrine deals with the subject of the life of Jesus Christ as the Son of God. There is but one Person : two natures. The hypostasis (personal subsistence) of Jesus Christ was the eternal Son of God who condescended to take human flesh through Mary. It will readily be seen that those who deny that Jesus had any existence prior to Mary conceiving him via the Holy Spirit, will deny this doctrine. Likewise, those who deny the doctrine of the incarnation (as in the Trinity) will deny the hypostatic union.

The Chalcedonian Definition (452) basically declared Jesus Christ to be one 'who' and two 'whats' - one person of two natures (or substances). Now, here's an important quote about this declaration.

"It may be conceded at once that the Definition is not an explanation of the mystery of the Incarnation. The very failure of the Definition to solve the insolvable is its best recommendation to our careful consideration. The framers of the Definition were not concerned so much to formulate a theory as to safeguard the truth from two attempted solutions of an erroneous character, and to preserve for us the truth hidden by both those errors." Christ in Eastern Christian Thought, John Myendorff, p. 38 (Crestwood, N.Y., St. Vladimir's Seminary Press 1987)

I give this quote to help show that your first question, "1. What is the difference between soul and spirit?" shows you are starting from a human point of view, hoping to sort out what applies to humanity in order to sort out what was uniquely done when "the Word became flesh" (John 1:14). The hypostatic union starts with deity in heaven, coming down to identify with humanity on earth. This was an utterly unique event. We will not find its like, nor its explanation by looking at ourselves.

Likewise with the second question, "2. ...In nature [Jesus] is God. God is spirit. Does anyone have any idea about the existence of Jesus's Soul and Spirit? Or He had a human Spirit?" This is to confuse God being Spirit, with the human spirit. God in heaven never ceased to be Spirit when the Son left heaven to become flesh. Yes, the man Jesus had a rational soul, but not at the expense of his deity. As the quote above points out, the Chalcedonian Definition of the hypostatic union cannot explain how this was achieved, only that it was. For those who would scoff, claiming that proves it's mere human invention, the opposite is the case. Had men dreamed this idea up, they would have been careful to have all the problems ironed out, presenting a smooth explanation. On the contrary, it was formed to protect belief in Christ from man-made ideas that corrupted the biblical gospel of Christ.

That is why I have not taken your two enumerated questions as the real basis for this answer. I have dealt with the hypostatic union, which is what this matter is all about. The matter of the human soul and the human spirit is a different matter, I would suggest, even though related. The right starting point should lead to the right conclusion, and the starting point is in heaven, when the Son condescended to come to earth, to so identify with us that he became one of us. There is no denial about his true humanity, but when denial as to his true deity arises, then debates are helped by considering the Chalcedonian Definition, the heart of which says:

"In agreement, therefore, with the holy fathers we all unanimously teach that we should confess that our Lord Jesus Chris is one and the same Son; the same perfect in Godhead and the same perfect in manhood, truly God and truly man, the same of a rational soul and body; consubstantial with the Father in Godhead and the same consubstantial with us in manhood; like us in all things except sin; begotten of the Father before all ages as regards his Godhead and in the last days the same, for us and for our salvation, begotten of the virgin Mary the Theotokos as regards his manhood; one and the same Christ, Son, Lord, only-begotten, made known in two natures without confusion, without change, without division, without separation; the difference of the natures being by no means removed because of the union but the property of each nature being preserved and coalescing in one person (prosopon) and one hypostasis, not parted or divided into two persons but one and the same Son, only-begotten, divine Word, the Lord Jesus Christ; as the prophets of old and Jesus Christ himself have taught us about him, and the creed of our fathers has handed down." (Ibid.) Approved and signed on October 25, 451.

EDIT - In response to a comment , it was because the biblical gospel began to be changed by some who wandered away from what it said about Jesus that the 'hypostatic union' explanation had to be put down in words that would prevent those ones corrupting the gospel. Those ones were attracted to pagan concepts, trying to bring those into their thinking about Jesus.