Is Mary the mother of that fully God baby?
Fully answered earlier in the thread.
She's not the mother of God.
Well sure. I said earlier that I personally did not have a problem with "Theotokos" (especially as opposed to "Christotokos") because I think I have an understanding of how it is being used by the people who are using it. In witnessing, I would not choose to first use the term "mother of God" UNLESS I was also led to go into a whole long explanation of what that meant. That could very well happen someday. In addition, our respective explanations would certainly be different, including the mechanics. We would also disagree on what the title says about Mary. :) However, on the simple point of whether Mary gave birth to the God-man, thereby she was His mother, and if that's what Theotokos means, then "yes".
Anyway, in the same breath I agree with the criticisms of the other Protestants here, in that such a term could very well lead to a wrong impression, especially in witnessing. It really would take a full explanation. But here, in this conversation, among you all, it doesn't bother me, (and of course many of the points have been discussed on this thread). Nobody here thinks that our Lord Jesus took on His divine nature after physical birth.