MBA/PGDM

No, it is not necessary but it will act as an added advantage in GD-PI as well as in placement process.

No, in distance education there is no need for entrance exam.

Hello,
The top four colleges for pursuing MBA, also having a low fee structure (tuition fees mentioned) are as follows:-
1. FMS, New Delhi - Rs 21k.
2. Sydenham (SIMSREE), Mumbai - Rs 1.38L.
3. Pumba, Pune - Rs 1.33L
4. JBIMS, Mumbai - Rs 6L.

Not really, as NDIM is neither a famous brand's name nor does it rank even within the top 50 B-schools across India. Choose it only if you do not have any other better choice left and/or are unwilling to prepare for the various MBA entrance exams once again.

Hello,
Being from a Science background, I think pursuing MBA in IT is the most suitable option for you. However, you can choose any specialization as per your interests and career goals. Kindly visit the given link to know in detail about the top five specializations in MBA.
https://www.shiksha.com/mba/articles/top-5-mba-specializations-in-india-blogId-3223

Hello,https://www.shiksha.com/mba/articles/20-mba-entrance-exams-you-can-take-this-year-blogId-11473 Kindly visit the given link, which will give you an idea about the possible dates of the various MBA entrance exams to held this year.

To appear for CAT, you need to be a graduate. I would suggest you to complete graduation through correspondence (you can do fast tract Graduation in 2 years), or complete BE to appear for CAT.

Yes, it is a very good combination. Even, I have studied till CS Executive and, then opted for MBA in finance for my career growth and job opportunities. If we do CS with MBA, the positive point will be, even if you fail to clear CS, you have job opportunities on the basis of MBA degree. The knowledge you get while doing CS of subjects like taxation, accounts, SEBI will be handy and will definitely play an important role in improving your knowledge and chance of getting job opportunities.
So, all the best take your decision accordingly.