You can get a tourist visa if you are studying at a 'givernment approved institution', not necessarily a university.Do you mean student visa?
Ni Hao Lyndsey! Welcome to IM!
You can take a look at the visa section of this forum. From my experience, I can say that quite a few friends have stayed in Calcutta for 6 months or more on tourist visa. As long as you stay away from formal university courses, I think you will be fine. If you do intend to go for proper university courses, then you'll need a students' visa.
So, with a normal tourist visa, IMHO, you can:
- Learn Bengali at RK Mission
- Take/give private tuitions
- Rent an apartment
Also, since you are searching for apartments, RK Mission provides decent accommodation at their Golpark centre. I don't have any idea about the criteria, but you can talk to them.
From my experience, I can say that quite a few friends have stayed in Calcutta for 6 months or more on tourist visa.