Why do theologians and philosophers suppose a connection between God's Infiniteness or Finiteness and Omnipresence, and Problem of Evil?

Muslim here, first look at this:

Isaiah 44:6 Thus saith the LORD the King of Israel, and his redeemer the LORD of hosts; I am the first, and I am the last; and beside me there is no God.

God is the First -> None existed with Him before.

God is the Last -> None will exist with Him when the Hour comes, i.e. the End of Time.

This is indeed; not a direct proof on God's eternity, but in Matthew 19:

16 And, behold, one came and said unto him, Good Master, what good thing shall I do, that I may have eternal life?

17 And he said unto him, Why callest thou me good? there is none good but one, that is, God: but if thou wilt enter into life, keep the commandments.

And:

25 When his disciples heard it, they were exceedingly amazed, saying, Who then can be saved?

26 But Jesus beheld them, and said unto them, With men this is impossible; but with God all things are possible.

Which denies the assumption of the limited god, and:

29 And every one that hath forsaken houses, or brethren, or sisters, or father, or mother, or wife, or children, or lands, for my name's sake, shall receive an hundredfold, and shall inherit everlasting life.

So if the Afterlife is eternal, then the One who will give it is definitely Eternal too.

I always view Omnipresence from the story of Moses, you know that Moses heard God's voice from the fire:

Deuteronomy 4:12 And the LORD spake unto you out of the midst of the fire: ye heard the voice of the words, but saw no similitude; only ye heard a voice.

But where was God exactly at that time?

Matthew 23

8 But be not ye called Rabbi: for one is your Master, even Christ; and all ye are brethren.

9 And call no man your father upon the earth: for one is your Father, which is in heaven.

So [in reality] God was not physically on the earth even when Moses heard His voice, which means God can control reality while not being physically apparent to someone inspecting around [like Jesus miracles], that's why Moses asked to see God and He [in turn] refused Moses request in Exodus 33:20.

You can say that God's Omnipresence [by definition] is His complete dominion over the universe we observe even when we can see His effect but not Him, and we can't think of God like a human who has our limits of control and presence, He can not be limited if He is Omnipotent.

The problem of evil is actually non-existent when we know that God created a Paradise [Matthew 26:29] and a Hell [Luke 12:4-5], it was already part of the plan, which means God held this life as a trial ground for the creation to make a future court [i.e. the Hour to come] for the righteous and the wrongdoer:

Luke 12:51 Suppose ye that I am come to give peace on earth? I tell you, Nay; but rather division:

That the God of our Lord Jesus Christ, the Father of glory, may give unto you the spirit of wisdom and revelation in the knowledge of him: The eyes of your understanding being enlightened; that ye may know what is the hope of his calling, and what the riches of the glory of his inheritance in the saints, And what is the exceeding greatness of his power to us-ward who believe, according to the working of his mighty power, Which he wrought in Christ, when he raised him from the dead, and set him at his own right hand in the heavenly places, Far above all principality, and power, and might, and dominion, and every name that is named, not only in this world, but also in that which is to come: And hath put all things under his feet, and gave him to be the head over all things to the church, Which is his body, the fulness of him that filleth all in all. - Ephesians 1:17-23

I believe that the above indicates infiniteness in both space (fills all in all) and consciousness (head over all things).

The next verse indicates infiniteness in space or, rather, an infiniteness that created space is unable to contain:

And now, O God of Israel, let thy word, I pray thee, be verified, which thou spakest unto thy servant David my father. But will God indeed dwell on the earth? behold, the heaven and heaven of heavens cannot contain thee; how much less this house that I have builded? - 1 Kings 8:26-27

As ever, there are theologians who will attempt to limit the Almighty in scope or in power, in knowledge or in attribute according to the limits of human wisdom. As ever, our biggest problem is that the God we conceive of is already too small in our conception. Our minds crumble in the face of eternity and infinity and, rather than fear Him who is both, we reason His immensity away.

He is omniscient, omnipresent, and omnipotent and nothing is hidden from the eyes of Him with whom we must make an accounting:

There remaineth therefore a rest to the people of God. For he that is entered into his rest, he also hath ceased from his own works, as God did from his. Let us labour therefore to enter into that rest, lest any man fall after the same example of unbelief. For the word of God is quick, and powerful, and sharper than any two-edged sword, piercing even to the dividing asunder of soul and spirit, and of the joints and marrow, and is a discerner of the thoughts and intents of the heart. Neither is there any creature that is not manifest in his sight: but all things are naked and opened unto the eyes of him with whom we have to do. - Hebrews 4:9-13

The only safety before the infinite, eternal Almighty One is not a safety of works (but this is just why we reason God to be smaller than He is...in order that we may perform adequately) but it is a safety of rest wherein we rest from our own works and believe in the works of God which He accomplished in Christ and wherein He rests:

For Christ is not entered into the holy places made with hands, which are the figures of the true; but into heaven itself, now to appear in the presence of God for us: Nor yet that he should offer himself often, as the high priest entereth into the holy place every year with blood of others; For then must he often have suffered since the foundation of the world: but now once in the end of the world hath he appeared to put away sin by the sacrifice of himself. And as it is appointed unto men once to die, but after this the judgment: So Christ was once offered to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation. - Hebrews 9:24-28