반 is the group of students in a room (they usually stay in one class the whole day). Example: 3-7. This would be 3학년 7반. Grade 3, room 7 (or literally class 7).
Let's take look at the hanja...學級, 학 is easy, used for something related to study. 급 means 등급 as in level/ranking. Looking at example sentences (I've maybe heard this word used once or twice in 2.5 years here), it looks like it could be used as 수업 or 빈 or 학년 almost like it's a general term. I've copied a few below.
그는 항상 학급에서 1위이다. - He's always at the top of his class. 이 학급에서 누가 가장 나이가 많지? - Who's the oldest in the class? 그는 성별로 학급을 나누었습니다. - He split up the class by gender. 영어의 초보자를 위하여 학급을 만들다. - I'm making a class for beginners English.
Sorry to bother but I've heard of '교실'. What is the difference between those two and '교실'?
They are the same meaning but 학급 is very formal and used mostly in letters or announcements from the school. 반 is more common.
Same meaning but 학급 is very formal and uses primarily in letters or announcements from the school. 반 is more common.