Science

B.Sc is better if you are not getting any college till date as here you do not need to worry more about the college as for campus selection college makes matter so you can go for B.Sc.

Those who have completed 3 year diploma course after matriculation are also eligible for BCA B.Sc. Course. For admission you must have passed in 3 year Diploma in a branch of Engineering from a polytechnic recognized institution with a minimum aggregate of 50% marks.

Any graduation will make you eligible for MBA provided you clear aptitude tests such as CAT/CMAT/MAT etc. as applicable to your institute of study.

Problems are unlikely, but exposure to statistics, research methodology, calculus, economics, accountancy etc. will make you feel better.

It has to be banking/finance related, you will have to search out for a person who will be able to guide your work. You may also attempt to clear NET or equivalent.

For doing an MBA any degree will make you eligible provide you clear aptitude tests such as MAT/CAT/CMAT etc. as applicable to the institute of your study. Prior exposure to statistics, research methodology, calculus/mathematics, economics, accountancy etc. will be an added advantage while doing an MBA. MBA is multidisciplinary, any way.

No, it's not possible.
You can't do B.Sc in mathematics without having maths in 12th.