I would say, "Das Mädchen probiert das Bier" as I have never heard anyone use "versuchen" for trying food or tasting anything.
Yes, I think it should be probiert.
When does one stop being a "Mädchen" and start being a "Jugendliche" or "Frau"? I imagine it is inappropriate to call a 16 year old Mädchen and that term is reserved for 12 and under? I have nothing to base that on, just a gut feeling.
I have asked Germans and generally speaking, you're about right. When a girl is in the last leg of the teens and becomes a woman seems to be the moment. Some guidelines there would be nice
veraltet = obsolete
veraltend = becoming obsolete