The particle で is used when indicating a location where the action takes place. が indicates a subject. The subject is implied here, but you could potentially add in (私が or 私達が). Subjects, if understood clearly through context, are usually not written/said though. Another use of で is that it indicates a "tool" used for a particular action. For example: "I wrote my homework in pen" = ペンで宿題を書きました。 "Since I'm bad at math, I solved the problems with a calculator = 計算に苦手なので、計算機で問題を解いていました。

どこで勉強しますか is correct. If you said どこが勉強しますか？ it sounds like "what place studies" and it goes like Place never study, people study. However You can say like this; どこが勉強するところですか？(Where is the place we can study?)