Engineering Entrance Exam

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

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
Sa

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

Click on the link given below and watch the video till end.
After watching the video follow the steps as per described in the video. At the end you could find the list of colleges that you might get for admission on your rank basis.
https://youtu.be/hOlit6Un7l0

Hello Reshma,
GATE is an entrance exam for admission for MTech or ME courses in many institutions in India. But, it's not for MSc.