Engineering Entrance Exam

Candidates appearing for the VITEEE should have secured an aggregate of 60% in physics, chemistry, and mathematics/biology in the qualifying examination (+2/intermediate).
You may refer the link below for more eligibility details:
http://chennai.vit.ac.in/admissions/ug/eligibility

For GATE exam there is no weightage for 12th marks. You should have a B.Tech degree only with a good score to appear for GATE exam.
For the eligibility details refer:
http://www.gate.iisc.ernet.in/?page_id=130

I'd suggest against taking up engineering if you're not sure of what you want to do, because it's a rat race out there, and you'll regret it later. I'd suggest you choose between the other two.

Try for private colleges which accept 12th scores like CGC Landran, Chitkara, Bhai Gurdas, etc.

Sorry to say but it's difficult for you to get a good government college at this rank. If your rank was under 1500 ST category then you would have chances to get a government college.

Hello,
Your rank is far beyond to get any government college via WBJEE, however check here to get more insights:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Kindly visit the link mentioned below:
https://www.shiksha.com/wbjee-college-predictor

No, you won't be able to get mechanical engineering at Thapar University but if you are interested in MBA also you can get dual mechanical degrees at Thapar University.

Hello,
Scholarships in MIT are need-based that is offered basis your financial background. Quite obviously you will be considered for a scholarship once you have been shortlisted and you will need an extraordinary profile to be considered. IIT JEE Advanced is not even required. You must take the SAT and SAT subject tests and the TOEFL. Apart from a very high academic percentile in 12th you must have an all-rounder profile and must have good scores in the SAT and TOEFL.