1. A lot of studens are studying in the study room.
(Can we use the term 'study' room' as a big place where students can study together? Do you have some other expressions for that?)
2. He is in the reading room with his friends to read books.
(Is it grammatical? Can we use 'reading room' as a place for reading books, textbooks, etc?)
1. I've used "study hall."
2. Yes. This is fine.