BBA

It does not happen like this. If there is any serious issue with the college or any other problems, this case may be possible. It all depends on both the colleges' policies, the college which you want to leave and the college you want to join.

One of the possible option is Avalon Academy, Patna.

University migration may not be possible. It depends on your university rules and regulations whether they can give migration and also on the university in which you want to take admission. College migration is possible within same university. University migration is provided only in special cases by UGC.

Most fo the colleges require at least 50% marks in 12th standard.

Manav Rachna is s good university with good placement records. They have a huge campus and good learning and study environment. Their faculty is also good. You can read the reviews through below link.
https://www.shiksha.com/mba/resources/college-reviews

IBPS bank PO is based on mental and logical reasoning test. The syllabus of IBPS PO exam consists of logical reasoning, general awareness, language ability test, quantitative analysis and data interpretation. There are no questions related to any specific subject. But pursuing BBA will help you to allocate time for preparation of Bank PO as this course a little bit easy as compared to other courses and you will be able to manage time easily.

It depends that on in which college or university you are pursuing your BBA from.