KGEC - Kalyani Government Engineering College

Yes, of course. For admission in JGEC and KGEC, you don't need to complete class 12th. But, for JU you need to have passed Class 12th.

I guess, it will be around 100-200 GMR for mechanical engineering.

With this rank, I hope you'll get IT in Kalyani Government Engineering College or Jalpaiguri Government Engineering College.
You may try for other government colleges for better or other streams.

I think, you'll get IT most probably and not CSE.

List of Government college which offer Lateral B.Tech through JELET:
Academy of Technology, Kolkata
Aryabhatta Institute of Engineering & Management, Durgapur
Bengal college of Engineering and Technology
Camellia School of Engineering and Technology
Institute of Science and Technology, Medinipur
MCKV Institute of Engineering, Howarth
Swami Vivekananda Institute of Science and Technology, Sonarpu
Source: http://entrance-exam.net/forum/diploma/list-government-engineering-colleges-offer-lateral-b-tech-through-jelet-india-1821805.html#ixzz5R2nvpsVU

Yes, there is ann ST quota for JELET candidates.

ST seats are very less in government colleges.
Only one in each engineering colleges.
Depends upon your trade rank and how many ST Candidates appeared for your Department.

Yes, you can get Kalyani Engineering College at this rank. There is 70% possibility you can get it.
All the best.

Kindly visit this link:
https://www.shiksha.com/b-tech/resources/wbjee-college-predictor