BBA

If you are interested in Maths, then go for B.Sc IT, otherwise go for BBA, because in sports you have to give your maximum time there. So, simultaneously you have to focus on your studies to get minimum qualified marks.

It is a really good course to study right now in India. It offers numerous opportunities for the students in academic growth and as a career. Most famous colleges for this course is the IITTM.

Actually both are really good. Both courses holds good at their respective places. It is the matter of choice of your interest. If you want to build career as an accountant or auditor and also if you are good at accounts then choose B.Com else if you are more interested in learning Management principles and it's applications, then go with BBA.

The second one is the most obvious answer. But this would generally depend on what the specialisation is.

Give entrance exam.

Yes, you can apply for CMAT exam you are eligible for that. For the applying process and more details you can go through this link https://www.shiksha.com/mba/cmat-exam.

No, sadly not. You will have to take a readmission that is from the 1st year itself. Also, maybe at the time of admission they will ask you to submit a gap certificate. That's it. However, if you want to change the college and really feel that it's worth it then go for it. Don't push the degree if you have found an opportunity somewhere else just because of the fear of a gap or so. All the best to you.

The total fees is INR 34,290, for more details check out the link below :
https://www.shiksha.com/bba/course/bachelor-of-business-administration-bba-the-bhawanipur-education-society-college-bhawanipur-kolkata-92965

First of all, you have analyze your keen interest whether it is computer related or business related. But, as I had done BBA now, and pursuing MBA is far better scope than BCA or MCA in terms of Placements, education, research and future perspective, you will get exposure in BBA technical as well as theoretical. All the best.