B.Sc

Miranda House is best for you because its placements are too good and it is one of the topmost colleges of Delhi University.

Please mention the location, otherwise it will not be easy to guide you.

Dear Neha,
You know well that B.Sc doesn't have any direct relationship with the banking sector.
1) General / Computer Science B.Sc: It will only count as a Bachelor's Degree and you ought to give the common exam that the bank takes before giving job offers.
2) B.Sc. Statistics (or economics): Will surely help you gain the higher job role in finance and economics division of any bank like commercial, forex or any investment bank. Hence, my suggestion is to go for the cores which have any direct relationship with the banking sector (like BBA, B.Com and B.A. in economics), etc.

You can join MBA just after clearing your B.Sc as a professional course. You just need to clear your Bachelors degree.

Yes, you can enroll for B.Sc nursing in JIPMER AIIMS and other institutes.

You can definitely apply for MBA after your backlog is cleared. I guess the institutes would look forward for your skills and abilities rather than the academic results always. Check out for the colleges of your choice and get the information about the same and also know the criteria for admission.