Yes.
I dunno about that last.
As for the first part, God the Son Incarnate is indeed the 2nd person of the Trinity, being He was from before He was born -- AND -- when He was born, thus ultimately, in that sense, Mary did give birth to the One whom we otherwise accept the description, was "fully man, and fully God", with there being no divisibility of those aspects -- when He existed in the form of a man.
What exactly we should think of Him now (other than God?) can be somewhat puzzling. He did say to his disciples (John 6:62)
On His Father's side, He was God.
And He was Jewish, on his mother's side.
Yet now -- has indeed returned to where He was "before" (like -- where He was before He was born in the likeness of sinful flesh making Himself of no reputation, taking the form of a bondservant, and coming in the likeness of men. (Romans 8:3, and Philippians 2:7).
Don't get me wrong ma, I'm not meaning to be coming across as lecturing to you, but instead am writing of Christological considerations. Perhaps someone out there in the interwebs could be edified. Meanwhile, this conversation is intruding upon the rest of the forum...
I don't believe it's an intrusion...
But I'm thinking that your position brings us to: did the 2nd person of the Trinity die on the Cross??? So far, I don't believe he did...