Exam

No, it depends on your percentage in class 12th.

You are likely to get NIT, but with average rank, LMNIIT with a decent branch, though don't go with NIT less than 15th position among them. Moreover, shortlist the colleges according to their last year cutoff.

Yes, you are likely to get the following branch in IIITD with your rank.
The ranks for different branches are:
1. Computer Science and Design- 9316.
2. Electronics & Communication Engineering-10870.
3. Information Technology & Social Sciences -10304.

Yes, the closing rank for general caste was 4173 last year, hence he is more likely to get into it.

Your VIT branches are decided by VITEEE. Hence, apply for VITEEE and qualify it and check that results to see which branch you get.

Yes, the closing rank for NIT,Trichy CSE for General category was 4173 in 2017, hence you are likely to get that.

Yes, you can apply for MANIT through JEE Mains. This is though an obvious as mains is primarily held for NIT's only.

Neil Menon's answer provides satisfactory details, and I don't differ when it comes to Classical Mechanics and Quantum Mechanics, but have a point to add about Special Relativity (classical):
I would say that to really appreciate Special Relativity, one needs to read Introduction to Special Relativit

Dear,
For your information, NATA is not required for admission in any interior design program . NATA is required for B. Architecture program.

Don't take civil through management quota, as there are no placements in civil branch.