Hi Elena18! as mukkapazza points out yes, in Italian, a "bicchiere" can mean a glass or a short plastic cup. The word in Italian is not used solely for a glass-material drinking object. I hope this helps clear up your doubt :)
because pieno is an adjective modifying "bicchiere" which is masculine. It is not modifying the feminine acqua.
If it was a cup of coffee you could say,
La tazza è piena di caffè.
Tazza is feminine, caffè is masculine. The adjective is modifying the subject.