BCA

I will suggest for UEM-Kolkata for the good education from experienced faculty members and good placement record. Visit the link:
https://www.shiksha.com/university/university-of-engineering-and-management-kolkata-47398

Hi Viren, it is difficult to say, since, every university has different levels of selectivity and different admission requirements. Based on the information you have provided, chances of admission in a highly ranked university are low. You should check less competitive countries too such as Belgium, Poland, Norway, etc.

It depends on where you wish to see yourself after the completion of the course. If you wish to be loyal to your stream and aim at becoming a system analyst or a programming specialist, then an MCA is preferable. If you are confident of your managerial skills and wish to climb the corporate ladder, then you may prefer an MBA. But to be still loyal to your stream, you may like to do an MBA in Systems/IT.

My opinion is that B.Sc (CS) is better than BCA for you.

In case you want to work in IT and ITES Industries based on your computing skills and degree, you may evaluate doing MBA IT. You may refer to the following link for a list of top MBA B-Schools in Chandigarh: https://googleweblight.com/i?u=https://www.shiksha.com/mba/ranking/top-mba-colleges-in-chandigarh-tricity/2-2-0-12292-0&grqid=ElRzwPAE&hl=en-IN

B.Sc (CS) is better than BCA.

Both MBA and MCA are good career options leading to long satisfying career. If you are technically oriented and good at programming then you may opt for MCA, else you may opt for MBA.

No, you can't do two courses at the same time and there's no benefit of doing so.
Try to focus on one subject.
Good luck.

Yes, it's possible in private colleges.
You can try for private colleges.
Good luck.