Colleges in Tamil Nadu

Yes, you can get admission in Sastra and even admission is based on 12th marks.
12th marks - 70% and JEE Mains - 30%
So, it's dependent on both.

No, It's not possible to get CSE in any of the NITs. You have to go with private institutes with this rank to get CSE. Use the college predictor to know which colleges you can apply. https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

There are very fewer chances for you to get admission in IITs.

Hi,
the cut-off for MAT is 580+composite score (percentile in MAT). You might be eligible for GD/PI.

The category will define the merit list of the students. The students will be called for counseling based on the scores. I could explain with the example saying Rank 1 to Rank 2000 will be put up in Category 1 and the category 2 will have rank holders between Rank 2001 to 3500 and the rest into cate

I guess you were questioning about fee structure. I can give you the fee structure for first 3 years. For Category 1 :Rs.96,000; Category 2: Rs. 1,59,000; Category 3: Rs. 1,92,000. It will change for fourth and fifth year for all three categories. Please visit VIT website for more details.