"We have spare time after the classes."
Translation:У нас есть свободное время после занятий.
Though it ends in я, время is a neutral word. it's an exception to the rule. I had the same issue with есть though. Maybe someone can chime in
This word also means 'there is.' For example: Здесь есть хлеб. (Here there is bread.)
Урок is a lesson where you are taught something. School classes are always called уроки.
Занятие has a broader meaning of "activity". Also, college lectures, labs, etc. are never called уроки, but rather занятия.