Engineering

Being from OBC category, you might get admission in both the campuses, but not sure about the fields.

Yes, you will be considered as OBC-NCL candidate from the other state quota. All the best.

Artificial Intelligence is a way of making a computer, a computer-controlled robot, or a software think intelligently, in the similar manner the intelligent humans think. Colleges in India-
IISC B
IITs
and very few private colleges. Prerequisites ( can be learned after joining the course)-
Good mathemat

Top Information Technology Colleges in India Accepting WBJEE scores are mentioned at the link provided below:
https://www.shiksha.com/b-tech/ranking/top-information-technology-colleges-in-india-accepting-wbjee/50-2-0-0-3044.

Admission is based on the rank obtained in JEE Mains. Interested candidates can apply online with required information. For further details regarding this course please refer to the link provided below:
https://www.shiksha.com/b-tech/course/b-e-in-computer-science-and-engineering-rajiv-gandhi-proudyo

Doing B.Sc. IT from a government or private college does not really matter. What matters is how much do you learn during the course and how do you hone your skills.

You can check out the eligibility from the below given link as per your suitable course:
https://www.shiksha.com/university/anna-university-Chennai-3084/admission
Best of luck.

FIITJEE is better and is the best. Its classroom programs are awesome. Study material being not up to the mark in a sense that most of the answers are wrong.