WBJEE

Yes, you can get E&TC on the basis of your OBC rank, and also you can get:
Computer Science & Engineering/Computer Science & Technology
Electronics & Communication Engineering/Electronics & Telecommunication Engineering
Information Technology
Electrical Engineering
Mechanical Engineering
Instrumentation Engineering/Instrumentation & Electronics Engineering
Civil Engineering
Chemical Engineering.

OBC rank is just for the reservation purpose.

You don't have to apply somewhere. Just go there and get the mock counselling done by experts.

Mock counselling of WBJEE is that system in which you are able to get a rough picture of what colleges you will get. It's purpose is to analyze the candidate about what seat he may get. No, it is not necessary to attend. One tip from my side will be to attend this as you will get a clear idea.

It's a Tuition fee waiver for poor JEE candidates. Students who've cracked West Bengal Joint Entrance Examinations WBJEE and their family income is less than Rs 2.5 Lacs a year can now avail a full tuition fee waiver in AICTE-approved colleges.

You can see your score on official WBJEE website.

Yes, that will be considered only if you have proper valid documents.

Yes, only Neotia University can give you CS with this rank.

Yes, you can get admission under TFW quota. I am listing some colleges, do check the list below:
Budge Institute of Technology
Murshidabad College of Engineering & Technology
Gargi Memorial Institute of Technology
MCKV Institute of Engineering
Bengal College of Engineering
Haldia Institute of Technology
Saroj Mohan Institute of Technology.

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.