Engineering Entrance Exam

Yes, domicile is essential.

Yes, you are eligible and you will get a lateral entry.

Your rank should be at least 5K.

Institutes like Aakash, FIITJEE help students like you and me who prepare for JEE, they charge you according to your marks obtained in admission test, the better you do less they charge or else better you join IIT programme in your college they may take 5000/-for your books or else you can even get them on internet free of cost.

Definitely, you should start preparing even if you get 100%
in the central board as the syllabus of 10th and JEE are different, moreover, JEE is harder when compared with 10th.

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

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.

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.

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