If Jesus is God, why does he ask for forgiveness in Luke 23:34?
Luke 23:34 And Jesus said: Father, forgive them, for they know not what they do.
You forgot to mention "forgiveness for others" - not as if he had sinned himself.
But why he asks it and not just gives it, is because he is man also.
If Jesus is God, why in Mark 12:39 Jesus said "Hear, O Israel: The Lord our God is one Lord." The words "our God" indicate that Jesus had a higher God over him, a stronger being than him. Jesus didn't say "Your God".
Mark 12:29 And Jesus answered him: The first commandment of all is, Hear, O Israel: the Lord thy God is one God.
You forgot to mention Jesus was quoting the words of Moses. Also Moses received them from God who, like Jesus used the words "thy God"="your God".
If Jesus was God, then why Mark 15:34 says "And at the ninth hour Jesus cried out in a loud voice, "Eloi, Eloi, lama sabachthani?"-which means "My God, my God, why have you forsaken me?"
Mark 15:34 And at the ninth hour, Jesus cried out with a loud voice, saying: Eloi, Eloi, lamma sabacthani? Which is, being interpreted, My God, my God, why hast thou forsaken me?
Because, he is man also and has been forsaken to crucifixion. And because he is quoting Psalm 22. His throat is too parched to say all of it.
If Jesus was God, then did Paul say in 1 Corinthians 8:6 Yet to us there is but one God, the Father, of whom are all things, and we unto him; and one Lord Jesus Christ, by whom are all things, and we by him.
He said that because every thing that exists is by the Son, as it is from the Father. I e precisely because Jesus was no mere man.
If Jesus was God, then why in John 20:17 "Jesus saith to her: Do not touch me, for I am not yet ascended to my Father. But go to my brethren, and say to them: I ascend to my Father and to your Father, to my God and your God."
Precisely because the Father is Father of the eternal Son in one way and of Creatures adopted to sonhood in another way.
If Jesus was God, then why in John 8:28 Jesus said "I do nothing of myself"? Can't God do anything he wills?
Here is the quote: Jesus therefore said to them: When you shall have lifted up the Son of man, then shall you know, that I am he, and that I do nothing of myself, but as the Father hath taught me, these things I speak:
He is talking about the perfect unity of will between Father and Son. And he is talking about an impossibility to displease the father which no creature has, next verse:
And he that sent me, is with me, and he hath not left me alone: for I do always the things that please him.
If Jesus was God, then why in John 14:28 Jesus said "My Father (God) is greater than I"?
The quote: You have heard that I said to you: I go away, and I come unto you. If you loved me, you would indeed be glad, because I go to the Father: for the Father is greater than I.
The comment from Douai Bible Online:  For the Father is greater than I: It is evident, that Christ our Lord speaks here of himself as he is made man: for as God he is equal to the Father. (See Phil. 2.) Any difficulty of understanding the meaning of these words will vanish, when the relative circumstances of the text here are considered: for Christ being at this time shortly to suffer death, signified to his apostles his human nature by these very words: for as God he could not die. And therefore as he was both God and man, it must follow that according to his humanity he was to die, which the apostles were soon to see and believe, as he expresses, ver. 29. And now I have told you before it come to pass: that when it shall come to pass, you may believe.
If Jesus was God, then why in Luke 23:46 Jesus said "Father into thy hands I commend my spirit"? (Video has, quite correctly and indication that these words were directed to God the Father).
Because he was man also.
If Jesus was God, then why in Mark 10:18 AND LUke 18:19 he said "why do you call me good, none is good but God"?
Mark 10:17 And when he was gone forth into the way, a certain man running up and kneeling before him, asked him, Good Master, what shall I do that I may receive life everlasting?  And Jesus said to him, Why callest thou me good? None is good but one, that is God.
He said it to someone who was no disciple. Who did not know he was God. Who was therefore a bit illogical.
Luke 18: And a certain ruler asked him, saying: Good master, what shall I do to possess everlasting life?  And Jesus said to him: Why dost thou call me good? None is good but God alone.
If Jesus was God, then why in Matthew 26:39 Jesus begged his God to have mercy on him and to pass the cup to death (kill Jesus in another words) before Jesus goes through the pain of crucifixion? (and same verse) ... why did he fall on his face and pray to his God?
If Jesus was God, then why in Matthew 24:36 Jesus said "No one knows about that day or hour, not even the angels in heaven, nor the Son, but only the Father." ...
Matthew 24:36 in DRBO has "But of that day and hour no one knoweth, not the angels of heaven, but the Father alone."
But if he had said "not even the Son", he would have been talking about his natural knowledge or of his mystical body which is the Church. By the way, this chapter indicates very well why if someone is looking for the Messiah to be already returned, that someone is very foolish. See these verses:
 Then if any man shall say to you: Lo here is Christ, or there, do not believe him.  For there shall arise false Christs and false prophets, and shall shew great signs and wonders, insomuch as to deceive (if possible) even the elect.  Behold I have told it to you, beforehand.
As for 26:39, there is a misquote, and here is the real one: " And going a little further, he fell upon his face, praying, and saying: My Father, if it be possible, let this chalice pass from me. Nevertheless not as I will, but as thou wilt."
He is praying the Father not to let him die. And he prays that because as a man (He is both God and Man, remember) He fears death (which belonged to Adam's children due to his sin, in which Jesus had no part) and fears the Cross.
Which also solves the next one, how he could have Fear of God according to Isaiah. As well as reference to St Paul's Letter to the Hebrews, 5:7.
If Jesus was God, then why in John 5:31 Jesus told his followers that if he bears witness of himself, then his record is not true?
He is not speaking to his followers, but to his enemies. Answer is, and same to following question about previous verse: Because he mentioned that the Bible, the word of God had given a witness of Him which even the Pharisees (to whom he talks, unless it is their followers or other unbelieving Jews) cannot deny the truth of. He is also saying there that the word of Moses is not just the word of mere men.
If Jesus was God, then why in John 5:36-38 Jesus said that God had assigned to Him work and God is a witness on Jesus?
John 5: But I have a greater testimony than that of John: for the works which the Father hath given me to perfect; the works themselves, which I do, give testimony of me, that the Father hath sent me.  And the Father himself who hath sent me, hath given testimony of me: neither have you heard his voice at any time, nor seen his shape.  And you have not his word abiding in you: for whom he hath sent, him you believe not.
He means not work as "assignment" but works as miracles. God by making his miracles testifies - that he is God. Jesus reminds his enemies that without God he could not have done the miracles.
As verse 37, the Pharisees saw Jesus in his Human Form and did not hear his word as the Voice of God. See beginning of passage:
John 5: Therefore did the Jews persecute Jesus, because he did these things on the sabbath.  But Jesus answered them: My Father worketh until now; and I work.  Hereupon therefore the Jews sought the more to kill him, because he did not only break the sabbath, but also said God was his Father, making himself equal to God. ...  For as the Father raiseth up the dead, and giveth life: so the Son also giveth life to whom he will.  For neither doth the Father judge any man, but hath given all judgment to the Son.  That all men may honour the Son, as they honour the Father. He who honoureth not the Son, honoureth not the Father, who hath sent him.
And after this the man who made the video tries to make a problem about the divinity from John 5:32? And especially as these words are adressed to his enemies, not to his followers! They had not ever heard the voice of God (in the Bible, in their hearts), and he knew it from how they received him.
If Jesus was God, then why did he pray to his God in Luke 5:16?
Again one where you must remember that he was man also. As eternal Son he could always contemplate the Father, and in his divine nature he was doing so all the time. BUt his human mind needed that too, and to his human mind human company was a distraction from that and he needed to go out into the desert for it.
If Jesus was God, of God cannot be tempted James 1:13 ...
That is not what it says there. James 1: Let no man, when he is tempted, say that he is tempted by God. For God is not a tempter of evils, and he tempteth no man.
The verses about Jesus BEING tempted do not say he was TEMPTING OTHERS.
Source for bold quotes
St Dominic's Day/HGL