Can I change my institute and university after getting admission in BE course?

Yes, you can. But, it depends upon the college criteria and available seats. Mostly, you can change your institute after the 2nd semester.

Yes, you can, but every institute has its own criteria and you need to fulfil the same.

Yes, you can. There are many institutions allowing you to change the college under the same university. In the case of a university, you might experience some problem.