WBJEE

Yes, you can get government colleges. I am listing top colleges do check:
Jadavpur University of Calcutta
Kalyani Government Engineering College
Heritage Institute of Technology
Government. College of Engineering & Textile Technology
Jalpaiguri Government Engineering College
University Institute of Technology.

No, you can't get admission if you are out of West Bengal with WBJEE. For the candidate who are outside West Bengal, you have to crack JEE Main and Advanced too.

No, you can't. You have to get caste certificate for admission.

Yes, with this rank, you can get MSIT, and also you can get all branch like electronic, electrical, civil, CS ,IT.

Yes, if you are not satisfied, then you should opt for 2nd round counseling.

Yes, on the basis of your SC rank, you can get government college.

Your fee will be around INR 94.5k per year.

On the basis of your TFW, you will get:
Techno India College of Technology
College Of Engineering and Management
Narula Institute of Technology
Bengal College of Engineering & Technology
Asansol Engineering College
Calcutta Institute of Engineering & Management
College Of Engineering and Management.

Check the below link for colleges you can expect at this rank-
https://www.shiksha.com/b-tech/resources/wbjee-college-predictor

Dr. B. C. Roy Engineering College, Durgapur is a self finance college. It is affiliated with West Bengal University of Technology. The college is approved by both All India Council for Technical Education (AICTE), Directorate of Technical Education (DTE) and Department of Higher Education, government of West Bengal.