Please excuse any typographical errors, but the only way I can answer questions is to not proof read them, since that process is extremely time consuming, for me.
The answer to your question as stated in paragraph 3; (So, the question is did Jesus become God's Son in the begetting in Mary or is he God's Son before he was begotten in Mary?), is both.
Now that I have you thoroughly confused let me explain that.
Jesus exists as a duality, by that I mean that Jesus exists as both human and Deity.
All Scripture is quoted from the New King James translation, unless otherwise noted.
- Jesus was born in the form of a human to the virgin Mary as is stated in:
Luke 1:35 And the angel answered and said to her, "The Holy Spirit will come upon you, and the power of the Highest will overshadow you; therefore, also, that Holy One who is to be born will be called the Son of God.
Luke 1:35 And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God.
That both humanity and deity were both present in the form of the man Jesus is evident in:
Matthew 8:28 and 29 When He had come to the other side, to the country of the Gergesenes, there met Him two demon-possessed men, coming out of the tombs, exceedingly fierce, so that no one could pass that way. 29 And suddenly they cried out, saying, "What have we to do with You, Jesus, You Son of God? Have You come here to torment us before the time?"
While these demons were speaking to the physical Jesus it is evident that they were keenly aware of the Deity of Jesus, not only calling him the son of God, but indicating that that they would be one day tormented, which takes place in:
Revelation 20:10 The devil, who deceived them, was cast into the lake of fire and brimstone where the beast and the false prophet are. And they will be tormented day and night forever and ever.
And even though the Devil's angels are not mentioned specifically, they too will be tormented day and night forever and ever, as indicated by Jesus in:
Matthew 25:41 "Then He will also say to those on the left hand, 'Depart from Me, you cursed, into the everlasting fire prepared for the devil and his angels:
So Jesus the deity (or if you prefer Spirit) was the son of God from before the begetting, and the human Jesus became the son of God at the begetting; therefore both are true.
Hope this helps