Engineering Entrance Exam

https://www.shiksha.com/b-tech/resources/wbjee-college-predictor
Check the colleges you can get with your rank.

There are very few seats for general in both the colleges. Also, in NIT, minimum board percentage should be 75%, so you will not get NIT.
For Sir JJ, the admissions are through 50% board + 50% your competitive scores. Your board percentage seems less, so the chances are very thin.

Yes, you can get into GSITS Indore with spot round admission. It is in top 100 in NIRF rankings. You can get into RGPV University (Bhopal). For more possibilities, I would suggest you going through some state universities and autonomous institutions as well. Also, if you have marks more than 100 then you can be into LMNIIT, Jaipur also, Rest, private and other government. Universities are there for which you need to clear their entrance.

Which branch do you want?

https://googleweblight.com/i?u=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&grqid=ASbgoVWA&s=1&hl=en-IN
Please go to the link I am sharing here to know about the colleges you can get.

These are the top 15 college for CS in terms of placement. All the colleges have an average placement of INR 3.8 lacs per annum:
Jadavpur
Kalyani Government
IEM
Heritage
Techno India Saltlake
Haldia Institute of Technology
Jalpaiguri Government
RCC Institute of Information Technology
Government College of Leather Technology
Meghnad Saha
Netaji Subhas
B. P. Poddar
Techno India Rajarhat
Coach Bihar Government
Purulia Government

Admissions are purely done on the JEE Mains rank so I'd suggest you to visit josaa.nic.in and check the previous year's cutoffs of your home state NITs as in most of the cases it is easier to get home state NIT because of home state quota.

No, but you can get ECE, IT and EE.

It depends on your branch of engineering.
CS - 2000
Civil - 30000
Mechanical - 40000
Please do share your interested branch of engineering so that I can help you in detail.

Hi Shivam,
There is no any chance of getting Thapar University. You may go for Chandigarh University, Sharda, etc.