One thing that seems to be a mysterey to you is the meaning of "Mother of God." as Catholics use the term. It is simply that Mary bore the man-God Jesus. It was through her that God became incarnate.
I understand the meaning. I object to the term. My earlier answer was in response to why I think using theotokos makes it more confusing. She did not give God a beginning. So therefore she is not his mother in the normal way that most folks would understand the word mother. Did God use her to become incarnate? Yes. I dislike the phrase though - plus, it and all the other "Mother titles" of Mary tend to elevate her to a level of devotion that she should not have. She is a role model. Was a virtuous woman. Is to be admired. She is not the queen of heaven, and given its context in Jeremiah would probably find the term abhorent. She is not the co-redemtrix. Her sorrow did not pay for my sins. Jesus's blood did. She is not a lot of things that have been thrown on her outside of Scripture. And don't you think that if the Holy Spirit comes and doesn't testify of Himself but of Jesus Christ, that Mary wouldn't draw attention and devotion to herself but to her Son?