University of Mumbai [MU]

CAT and MAT entrance would be the best option if you want to make career in management. I would like to suggest you to crack these entrance exams and get admission in top B-Schoold which will definitely help you achieve your goals.
Best of luck.

You need not to worry about that.
The professors who are taking your interview round will speak in Hindi if you'll insist.
Just focus on your test and all the best for your future.

Yes, you are eligible to do M.Sc in maths.

No, to get a degree you have to complete full 3-years B.Com course.

You can't do a BA in 1 year and this not a legal way to get a degree. Yes, Institute of distance and open learning provides distance education mode. If you are looking for a one-year bachelor course then look for the foreign university as they offer a one-year bachelor degree. Although you shouldn't look for a one-year degree course foreign universities are the option you have. You can also look for below options also:-
1. Amity University
2. Annamalai University
3. Mewar University
4. Suresh Gyan Vihar University
5. JIMS
6. NMIMS
Regards

Mumbai University offers distance learning programmes. B.Sc Computer Science is also offered. But, as per me, if you go to pursue it now, you will have to complete the first two years too again in correspondence.
Also, try to enquire at IGNOU. They might have some provisions which might help you.
All the best.