Can you read again what you have written here? How does "the Father became the Son" and "Gave His only begotten Son" harmonise in any way whatsoever?
And how does "the Father became the Son" not deny a Father Son relationship? Read John17 and tell me how (fify) your scenario makes sense.
In v.3, is Jesus the only true God; or is it only the Father? Is Jesus a false god? No; because the word "and" in that verse is "kai", which can be translated "even".
In v.5, my position has to do with Ephesians 4:10. There is the pre-incarnate Jesus (the Father) dwelling in eternity (outside of time). The after-incarnate Jesus (the Holy Ghost) has ascended to be outside of time also; so you have the
one Spirit (Ephesians 4:4, John 4:23-24, John 7:39) dwelling next to Himself in eternity. Now the Son may or may not be confined to time; although it is written that He ascended to fill all things (and therefore would also be outside of time in His human body) (see 1 John 4:1-3, 2 John 1:7).
The point being, that before Jesus descended, He was dwelling next to the Father who existed in the form of the (after-incarnate) Holy Ghost. And after He ascends, He will dwell next to the Father identified as the 1st Person of the Trinity (the pre-incarnate Christ).
As for your first question, Jesus said to His former self after descending to dwell in a human body, (Hebrews 10:5),
Wherefore when he cometh into the world, he saith, sacrifice and offering thou wouldest not, but a body has thou prepared me:
God gave His only begotten Son (see Isaiah 9:6 for the identity of this son, with Deuteronomy 6:4; Ephesians 4:5, Mark 12:29 (kjv), Matthew 11:25, Luke 10:21, 1 Corinthians 12:3, 1 Corinthians 8:6). The Son that was given was a distinct Person from the Father, but was the continuation of the Father, in that God descended to become a Man. God, in 1 Corinthians 8:6, is identified as the Father, and Jesus is identified as the Lord. Again we have the word "kai" in that statement; however if you separate Jesus from being the Father in that verse then He is not God: He is merely the Lord. But we know that the Father is the Lord (Matthew 11:25 and Luke 10:21) and therefore since Jesus is also the Lord He must be the Father; since there is only one Lord (Ephesians 4:5, 1 Corinthians 8:6; and Jude 1:4, which also contains the Greek word kai in between "only Lord God" and "our Lord Jesus Christ' and therefore the preposition in Greek means "even". The point being that there is only one Lord God, even our Lord Jesus Christ). Also in James 3:9, Romans 15:6, and 1 Corinthians 8:6 God is identified as being the Father; not the Son. And that the Son is identified as God in Hebrews 1:8-9 therefore indicates that the Son is the Father incarnated; a distinct individual from the Father and yet the same Person.
So God sent His only begotten Son to die for us. That Jesus is the Son of the Father is identified through the hypostatic union; the fact that He is the Son is identified by the fact that He is Deity in humanity.
The Father couldn't die for us because He was God outside of time, dwelling in eternity and such a being cannot die. But God sent His only begotten Son (He became a Man) because if he could only take on the nature of a human being He would be able to die for the sin(s) of the world.
But I reject this idea that the Father created an eternal mirror and Jesus was begotten through the existence of this mirror. The concept helps us to understand how God can be triune and that is all. Because Jesus was begotten in the hypostatic union; then ascended to exist outside of time and therefore exists in eternity next to the Father. But the origin of the Son is in that the Holy Ghost ("the Word" (?)--John 1:1, John 1:14) became one with the egg in the virgin Mary (Luke 1:35); and therefore the Holy Ghost became a Man.
So then, God gave to us in death the Person who came to dwell in the human body of Jesus (John 4:23-24, John 14:7-11) and it was the body of Jesus (and His soul--Isaiah 53:10) that God gave up for humanity when Jesus died on the Cross. Now the Spirit of Jesus did not die except in that He was separated from His human body.
I would ask you the following question: Did 1/3 of God descend to become a Man, or did God descend to become a Man?
In the concept of an eternally begotten Son, you have the problem either of there being a God beside Jehovah (see Isaiah 45:5, Isaiah 45:18, and Isaiah 45:21-22) or you have the problem of 1/3 of God descending to become a Man.
Now in the scenario that I present to you, the God that is beside Jehovah is Jehovah: the Son is the Father. But in some circles where they say they believe in the Trinity, they do not believe in the true Trinity but rather in Tritheism. To them, the Son is not only distinct from the Father, He is a separate God entirely.