NIT

Yes, try chemical engineering in the top three NITs either Warangal, Trichy or Surathkal, then I can tell you that the next best choice will be NIT, Surat, because it has a very good placement statistics.

With 65% marks in class 12th and with your good score in JEE Mains, you can apply for an NIT.

No, admission to NITs is only done through Jee Mains.

NIT-Trichy would be best for ICE.

As per the recent circular and news, below is the fee structure for 1 year:
1) SC/ST/PH : Full fee wavier
2) OBC, GENERAL : Family income 1 lpa : Full fee wavier.
3) OBC, GENERAL : Family income 5 lpa : 41k
4) Others : 1.25 lpa.
*lpa = lakhs per annum

If you feel there was some good reason that you couldn't perform well in JEE, then only you should go for it. Because 2 years drop will make a big difference for your career as it will shift 2 years ahead. And there is no surety if you could perform well in the next year's attempt.

Yes of course, it is one of the oldest engineering colleges in India. while many NITs are newly established and don't even has proper faculties and campus.

https://www.shiksha.com/b-tech/resources/upsee-college-predictor
Go through this, you will get to know about the results more better way and very accurately.
All the best.

Hello Keerthi,
You need to have atleast 75% in boards for taking admission into any NIT, so firstly clear all your papers and then look forward to taking admission in any colleges.