Jesus is equally God while still not God the father as well as not being God the Holy Spirit. They are three separate entities that all form the single God-head. John's gospels shows this to us.
"In the beginning was the Word, and the Word was with God, and the
Word was God. 2 He was in the beginning with God. 3 All things were
made through Him, and without Him nothing was made that was made. 4 In
Him was life, and the life was the light of men. 5 And the light
shines in the darkness, and the darkness did not comprehend it. 6
There was a man sent from God, whose name was John. 7 This man came
for a witness, to bear witness of the Light, that all through him
might believe. 8 He was not that Light, but was sent to bear witness
of that Light. 9 That was the true Light which gives light to every
man coming into the world.10 He was in the world, and the world was
made through Him, and the world did not know Him. 11 He came to His
own, and His own did not receive Him. 12 But as many as received Him,
to them He gave the right to become children of God, to those who
believe in His name: 13 who were born, not of blood, nor of the will
of the flesh, nor of the will of man, but of God. 14 And the Word
became flesh and dwelt among us, and we beheld His glory, the glory as
of the only begotten of the Father, full of grace and truth." - John
So once we understand that Jesus was not merely talking to Himself in Gethsemane nor upon the Cross. The question becomes. How could Jesus, being part of the God head, ask to be spared from that which he knew he must do?
Answer. Because while being 100% God he was also 100% man while in the flesh. The bible says that he felt every temptation, knew every pain that man feels. Nothing was withheld from him. So then once we understand that we can ask ourselves what person wouldn't beg to spared of such a painful way to die. Then we are also shown a beautiful example of obedience in that Christ said, "Not my will, but yours." Even knowing what awaited him he obeyed God.
Now to the second part of the question Why would he ask why he was forsaken? Because for the first and only time in eternity. Christ was separated from God's presence. All the sins of all mankind were placed upon Jesus. God is so Holy that he -can not- be in the presence of sin. He can't. It's not an option. Even for the love of his only begotten. Therefore Jesus was indeed forsaken in that instance.
Alternatively, Jesus was fulfilling a prophetic scripture in his crying out as well.
"My God, My God, why have You forsaken Me?.." -Psalm 22:1
I hope this helps. God bless