BBA

No, it's a 3 years programme.

Yes, you can do that.

Here is the list of few colleges-
St Xavier's College, Kolkata. THA Kolkata - The Heritage Academy. St Xavier's University, Kolkata. Haldia Institute of Management, Haldia. Pharmaceutical Management
Subhas Bose Institute of Hotel Management, Kolkata
Seacom Management College, Howrah.

Here is the list of few colleges-
Presidency university
GITAM Hyderabad business school
GEMS Tirupati
PIMR Indore
Jindal Global Business School
Mount Carmel College.

The fee for BBA at DU is INR 25,025.

INR 2.86 lacs (for 3 years).

Applied Maths doesn't count for DU JAT.

You need to confirm this from your college's placement cell whether they are providing placement for your course or not.

It depends upon the college basically. There are some colleges that provide coed education as well.

Both are good. It depends a lot on what you want to do. In my personal opinion, Shaheed Sukhdev BMS is better.