Ranchi

Can't find out in Ranchi but yes for different cities are available
National Institute of Event Management, Mumbai, Vile Parle West
Mumbai University, Mumbai
Impact Institute of Event Management - [IIEM], Delhi
Apeejay Institute of Mass Communication, New Delhi
Pacific University, Udaipur.

Your JEE rank is good, and you will get NIT college. To know which college, you may get use Shiksha JEE college predictor tool. Here is the link. https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

College does not offer BCA (Bachelor in Computer Application) course. A very similar and equivalent Bachelor's degree course is offered here. It is B.Sc in Computer Application. There is no cut-off declared officially. Cut-off varies every year. It depends on the performance of the candidates in the entrance exam that year.

Refer the below links :
https://www.shiksha.com/accounting-commerce/colleges/b-com-hons-colleges-Kolkata
https://www.shiksha.com/accounting-commerce/colleges/b-com-colleges-Ranchi.

You can refer Guide for BBA/BBS/BBM 2019 (English, Paperback, Arihant Expert), BBA entrance complete book paperback 2018-By Chandresh Agrawal (author), Chandresh Agrawal & Nandini books (editor), BBA/BCA/BHM/Integrated MBA Exam Guide by RPH Editorial Board Paperback, etc.

For which course do you wish to apply?

Though your score is less but still you can convert as it is totally dependent on how you perform in GD-PI. Prepare well, make your communication skills strong enough. Hope this helps.

Yes it is mandatory to pass in all the subjects to go for any college you want. You cannot proceed ahead, if you don't pass.