Exam

IES is an average college for pursuing PGDM with the average package being around Rs. 5-6 LPA. With 79 percentile in the CET, yes, you are eligible.

The cut-off for PGDM in SIES is around 75 percentile. In case, you got more than that percentile in the CET, you would've received an interview call.

Kindly visit this link:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

No, you have to take it along with you.

Hello Madhava,
You have good chances of getting a seat at SASTRA University. However, the branch which you can get is difficult to say since, the competition is very high. Hence, you may try your best at the counseling to get the branch you wish for.

If you have not cleared JEE Mains then you have chances of pursuing an engineering degree from most respected universities like BITS, VIT, SRM, SASTRA and many more state engineering colleges conducting entrance exams like EAMCET, WBJEE, MH-CET, COMEDK, etc.
Do not worry about JEE Mains. if you do well in above-mentioned exams, you can get a good college.

Yes, this rank is okay to get into NIT. I would suggest you take admission in IIIT or IISER this will be a good choice. If you are interested in research then go for IISER.

Yes, you will get good campuses in Coimbatore for CSE. Some of the best campuses in Coimbatore for CSE are Sri Krishna, Dhanalakshmi Sreenivasan, PSG, etc.

There is no syllabus for any entrance exam. I will say download the syllabus of B.Sc and last 5 question papers and prepare well.
All the best for your preparation.