Is this a private university or comes under Pune University?

It actually depends on which course you are talking of. Every College has some + and -. You can go for Bharati College.

I have completed my B.Sc Animation and Gaming from this college. This is the worst college i request you to not join this college. Wasted my 3 years and lots of money here.

For the clarification, you need to complete that first.

You can be eligible to apply for B.Sc in Animation.

Yes, you might get admission for B.Sc in direct second year although it depends on the college and varies from one to the other.