CBSE 12th

Yes, you can go for NID. Stream does not matter in UG. Application is out for the entrance session 18-19.

Yes, you can go for B.Sc Maths (Hons.), after class 12th. Some colleges though insists of having a science background, but then there are colleges those who accept. if a student has maths as one of their subjects. I guess Delhi University allows you for this, but you need to check out for their cut off for the same.

You have to give BITSAT, as BITS conduct their own exam. Improve your class 12th percentage and clear the cutoff.

No, you are not eligible for MCA. To pursue MCA, the eligibility is to have BCA degree or any Bachelor's degree.

There is no any restrictions in taking or choosing any course or subjects in class 11th. So, choose anything on your passion and focus on it. Enjoy and learn the subject carefully.

You have following options after Commerce in 12th class:
(a) Commerce Graduation (B.Com or B.Com (Hons))
(b) CA
(c) CS
(d) BA (Hons.) Economics
(e) BBA/ BBE/BMS
(f) BCA
(g) Hotel Management
(h) Fashion designing etc.
(I) Change to humanities or fine arts
(j) Five years integrated Law etc.
You can also join Indian Army by appearing for NDA exam conducted by UPSC. All career options are good and their own pros and cons. You must choose career based on your interests to excel in professional life.

If you are looking for commerce only, there are many options to choose. You can go for BBA, B.Com or BBA IB. Afterwards, you can also do MBA in finance department and if commerce is not your cup of your tea then there are other options as well.

There are a lot of universities which offer integrated M.Sc. ISRO, IISER, IISC are some of those which are the best.