NIT

You can visit this link:
https://www.shiksha.com/college-predictor

Check what colleges you can get into, use the link below:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993

NITs are centrally funded institutes and offer you better technical environment with some good laboratories and highly experienced teachers.

Yes , you are very much eligible as there are many private colleges. Our college offers B.E courses in CSE, ECE, EEE, ME, ISE & Civil. For further details, kindly look into our college website www.citech.edu.in. Thank you.

Click on the link for more details:-https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india-accepting-jee-mains/44-2-0-0-6244

JEE Mains and you have to secure above 200 marks to get good NITs or IIITs. You have to take PCM in 12th and must clear the same with at least 75% to appear for IIT JEE. If you score less than 75% then you cant appear for JEE Mains. So, also reappear for 12th to appear for JEE Mains.

If you wish to pursue B.Tech then you'll have to write JEE Mains and if you wish to get M.Tech from NIT, you'll have to write GATE. Other than that, there is a scheme called DASA for NRI students admission into NITs.

Hello Sagar,
If you are a resident of Delhi, you can get admission in one of these institutions, otherwise it is quite difficult. You may refer link also:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

You have bright chances to get DTU/NSIT if you are a Delhi resident.
9757 OBC rank is enough to get you DTU/NSIT. But, I can't predict what kind of course will be offered to you in counselling round. So, wait for the JAC counselling.

Predictor tool by Shiksha. This will help you to predict the college according to your rank/percentile:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.