West Bengal

IIM-Kolkata is top ranked institute (Rank-3 in India)
IIFT Kolkata: Indian Institute of Foreign Trade
MDI Murshidabad: Management Development Institute
GBS Kolkata: Globsyn Business School, Kolkata
Calcutta Business School, Kolkata
Xavier Business School (XBS), St Xaviers University, Kolkata
IISWBM Kolkata: Indian Institute of Social Welfare & Business Management (Ranked around 70 in India)
IMI Kolkata: International Management Institute (Ranked around 55 in India)
IIBS Kolkata: International Institute of Business Studies
IIBS Kolkata: International Institute of Business Studies
Praxis Business School.

No, there is less chances to any institute which don't have any age limit for student.

Visit the link below :
https://www.shiksha.com/college/st-xavier-s-college-Kolkata-park-street-23242.

Kindly visit this link:
https://www.shiksha.com/mba/colleges/mba-colleges-kolkata

https://www.iiqf.org/tiu-courses/data-science/certificate-program-data-science.html
Visit and explore
All the best.

No, you need to appear for WBJEE to pursue B.Tech (4 years) in any branch in MAKAUT University.

Budge Institute of Technology will be better.

You can consider IIOM-Indian Institute of Office Management.

Hello Soumya,
You can get admission in IEM. You will probably not get CSE but can get other branches like IT, ECE, EEE, EE or ME. In IEM only 10% seats are allotted for admission through JEE Main. So, it depends on luck.