NIT

With this rank, it will be very difficult for you to get a seat in a National Institute of Technology. You may get Integrated B.Sc-M.Sc courses in NIT,Patna, Rourkela and Agartala.

With those marks in JEE Advanced, I think getting into it is a bit difficult, and with a rank of 6500, you can get a good branch at top 6 or 7 NIT.

In my opinion, dual degree courses in NITs are not too bad, if your rank is not too good. But, if your rank is good , go for B.Tech and after B.Tech , clear GATE exam and opt IIT, if you still have to do M.Tech.

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.

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.