The term "first mother" has started to be used in adoption-related discourse. To you, does it imply a "first mother" is still that child's mother?

No. "First" implies sequential, like in "first wife and second wife." A woman who has surrendered a child for adoption is no longer that child's mother.

Yes. "First " implies concurrent, like in "first child and second child." A woman who has surrendered a child for adoption is still that child's mother.