West Bengal

As per AIMK guidelines 50 percentile is criteria for army category students and 70 percentile for general category students in CAT but students who have scored less applies as well and in most of the cases get selected for further process. People are generally judged on the basis of GD and PI regardless of your percentile.
So I would suggest that you can go for it as the chances are equally high.

Sanhita, don't worry. Many government as well as private universities giving admission for B.Ed without entrance but be sure that you have sufficient percentage to get admission because most of the universities select students on the basis of merit. In Kolkata, some universities give admission without entrance exam. You can try for that.

College change or university change after first year is completely dependent on college and university norms, some university allow it and some won't plus you need to have good scores in first year to apply for the same. For further details contact the college authorities.

Follow the link below and filter colleges according to fees:
https://www.shiksha.com/it-software/colleges/bca-colleges-india?uaf[]=location&ts=20780472&rf=filters&ct[]=130&bc[]=33&ed[]=et_20

XIME, Bangalore should be the best of the lot owing to the batch size and good faculty!