1. 재미있는공부하다
This one sounds most proper.
2. 재미있는공부하게다
Wrong. 재미있는 공부하겠다 is right in past meaning.
3. 재미있는공부하기다
We use -하기다. but in this context, very unnatural.
4. 재미있는공부하가 있다
Wrong. 공부하고 있다 is right in the meaning of present doing.
5. 재미있는공부하는 있다
Wrong.
6. 재미있는공부가 있다
There is a interesting study.
7. 재미있는공부는 있다
There is a interesting study.
6-7's is little different in nuance.
6 doesn't imply any meaning except that there is a interesting study.
but 7 imply that other thinks there is no interesting study or someone already told that there isn't, so you wanna oppose it.