NIT

With general, you'll get NIT Pondicherry, Silchar or Manipur with mining and related such branches (non-technical).
Also, it's not worth getting into these, spending 4 years and a huge fee as well.
The best I can suggest is LMNIIT where you can easily get mechanical or civil easily.
Best of luck.

Dear,
With such rank, I don't think you'll get admission in NIT or IIIT in the CSE branch, but you can go through the previous year data on JoSAA website.
Hope for the best. All the best.

Yes, of course, you deserve admission in NIT. As per my information, you are eligible for admission in the best colleges.
For more information, you can go through the last year's seat allocation details at JoSAA website.
All the best.

I don't know about CBSE but as per my experience of HSC board, you need to contact your school from where you appeared for 12th. The form is same as the regular form of 12th, you just have to tick class improvement instead of fresh while filling it. You can appear for class improvement two times, in July/Oct and next Feb/Mar.
Hope this will help you.

Please check out this website for more information regarding the opening and closing ranks in various NITs in the past two years:
https://josaa.nic.in/Result/result/OpeningClosingRank.aspx
The minimum percentage required in the 12th class board exams is 75%. I will pass on the information if I get to know more.
All the best!

Yes, you have a high chance of getting a decent NIT. Your rank is fine and since you belong to a reserved category, you will have no trouble getting a good college.

National Institute Of Technology is one of the best engineering college in India. If you want to be an engineer, and want to do something in this field, NIT would be a better opportunity for you. It has an international focus on development of their student's personality and ability. If you talk about future, it is in your hand totally. NIT will give you atmosphere, resources and knowledge rest is in your hand.

JEE paper 1 marks are responsible for NITs and CFTIs. Your 2 paper marks are responsible for IITs only.

There are several number of NIT colleges near Kolkata. Some of them are:
Narula institute of technology
Indian Institute of engineering Science and Technology
Government College Of Engineering and Leather Technology
Calcutta institute of Engineering and Technology

Sorry, but this score is not enough for getting into NIT. But you can get into some good private campus.NIT, Suratkal is very famous and students with a good rank below 3000 will get admitted each and every year.