JEE

Yes you can get admission in NIT but branch may differ from your choice. However in low NIT's you can get even good branch also. Now for taking seat in IIT you should first clear JEE advance examination then according that rank you can get admission in IIT. Here are few NIT's where there ia a chance that you can get seat :
NIT Jalandhar : here you can get Industrial and Production Engineering
NIT Durgapur: here Biotechnology you can get
NIT Nagaland: Here you can get Electronics and Instrumental engineering
NIT Raipur: Biotechnology you can get here
NIT Agartala: Production engineering you can get here
There may be few more colleges.

You will not get IIT or NIT because your all india rank is high. But you can get into a good private college. You can search colleges in Haryana and NCR area like gurugram, Faridabad, kurukshetra, Noida etc.

You can get admission in a state government college mostly but branch will be not too good. In central government college there is very few chance that you will get any seat, so you should try in government college of your state only.

Dear aspirant, Glad to meet you. JEE Main College Predictor 2022:
Enter your JEE Main 2022 Percentile or Rank to predict colleges that you can get admission in
Updated with Closing rank from 2021, 2020 and 2019
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Kindly visit this link
https://www.shiksha.com/engineering/jee-main-college-predictor
Hope it helps. If you found it useful then upvote or thumbs up my answer. Good luck.

Yes, JEE Mains rank is used for counselling in many colleges mostly government colleges.

In my opinion, you can get MNIT Jaipur. Congratulations on your good rank
To confirm just go through this link and fill out the required details
College predictor in shiksha
https://www.shiksha.com/college-predictor

If your JEE rank is below 25,000 then you have chances to get a CSE seat with your score. Otherwise, you will definitely get CS related branches. All the best.

There are chances to get into sastra with your score but you will hold that when you wait till 3rd round of counseling. All the best.

You can try for any branch seat in kumbakonam campus of sastra, you have chances to get a seat with your score.