As to the other, I don't know how to go further. Yeah, every other mother precedes what she bears. But we're talking about the Incarnation here, so we have to expect some rule stretching.
Jesus is God, Mary bore Jesus, therefore Mary bore God. God the Son is God. Jesus is God the Son. Mary bore God the Son. etc. You say that MUST mean Mary pre-exists God. I say no there's one other thing it COULD mean, that God, who pre-existed Mary, was content to be born of her in the miracle of the Incarnation. And it turns out that that's what most Christians say about the Incarnation. "When thou tookest upon thee to deliver Man, thou didst not abhor the Virgin's womb," and so forth. SO we say that to Call Mary the Mother of God is to say what has "always" been believed about the Incarnation.
I think we've pretty much worn this one out. Neither of us is saying anything new.
Makes logical sense.
Jesus is God. Mary is his mother. Mothers precede that which they bear. Therefore Mary precedes God.