Engineering

You have good rank with this rank. You can get Jadavpur University for CSE. Simply lock this option at time of counseling and after allotment, visit college and get admission.

It is INR 1,65,000 for all branches irrespective of rank.

No, with this rank you can't get Government College, but I am listing some colleges, do check the list below:
Hooghly Engineering & Technology College
Netaji Subhas Engineering College
Brainware Group of Institutions-Savita Devi Education Trust
Dr. B. C. Roy Engineering College
Guru Nanak Institute Of Te

It depends on the availability of seats at the time of counselling
Hope, you may get seat.

You'll get all branches like:
Computer Science & Engineering/Computer Science & Technology
Electronics & Communication Engineering/Electronics & Telecommunication Engineering
Electrical Engineering
Information Technology
Mechanical Engineering
Instrumentation Engineering/Instrumentation & Electronics Engi

Eligibility Criteria (Qualifying Exam)
Pass with 50% aggregate marks in class 10th (with Mathematics, Science and English)or equivalent.
For a candidate, who has not studied English as a subject, the condition of English may be waived off provided the candidate in his qualifying exam has studied in En

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

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.