Good question ! "Tu puella est" doesn't agree. "Est" is the third person singular of "to be" in Latin. So it doesn't match "tu" and should be es. It would be in English as if we said you is a girl. Hope this helps!
Both "femina" and "mulier" mean woman, but "mulier" can also mean wife. Curiously, in my mother tongue the modern form of "mulier" only means wife while that of "femina" is a formal/old fashioned way of saying woman.