IIIT

You have not given your JEE Mains rank so we are not able to find any college suitable to you. So, find it yourself. I am giving the link to you:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=6540165.

You have good chances of getting NITs. Try JEE college predictor to get more information and insight about college which you can get on the basis of your rank-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=4067795.

Try JEE college predictor to get more information and insight about college which you can get on the basis of your rank-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=4067795.

Just follow the link to predict the college which best suits you according to your rank-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7476690
Best of luck!

You won't get any NITs. You can get colleges of your state, maybe even government ones. Try JEE college predictor to get more information and insight about college which you can get on the basis of your rank-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=4067795.

No. The order goes like this:
IIT
IIIT
NIT
GFTIs
So, IIIT is better than NIT. But, I suggest you to not choose according to this because it may differ from few respects. So, choose when you are satisfied. Also, if you are getting NIT, then enroll for it whether it is very far away from your home or it is a new NIT.
Best of luck.

You might come across certain difficulties in dropping 2 years as with your age you won't be able to apply to some colleges. You should consider you age as a factor first and if you think you can do well by dropping twice you should go ahead with your plan.
good luck.

It will depend on Category. For General, there will be less marks for NIT.

With this score, you can't get any IIIT for CSE. You can try for lower branches in IIIT.

For IIT u will have to give JEE Advance and on the basis of JEE main u can get NIT and other gov or private college.