BBA

For BBA JIMS Rohini Sector 3 is a good option because it is one of the top 50 MBA colleges in India (40th).

INSPIRO KAS is a good institution with sincere teachers. You will get a good understanding of the topics and accordingly others felt that their environment is also conductive for learning.

You can consider following:
AIIMS Institute
Archarya Bangalore
Shoolini university
ISBR Business school
Guru kashi university
GD Goenka University.

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.