UPCAT

Yes, if you are a particularly looking for BBD, then yes you can get BBD, but also you have better option available for MBA. By the way, I am listing some colleges do check:
Jaipuria Institute of Management
B. N. College Of Engineering and Technology
Institute of Environment & Management
Sherwood College of Management
R. R. Institute of Modern Technology

You need to pass out the class 12th then apply for UPSEE.

Documents will usually depend on the course you are taking. But most commonly these documents will be required.
1. 10th Marksheet and Certificate
2. 12th Marksheet and Certificate
3. Any other course degree or certificate pursued in between.
4. Self declaration for Anti Ragging
5. Address, Birth and Caste Certificate as required.
6. Several photos
7. Declaration if there was a gap between academic education with the stated reason.
8. TC or Migration Certificate
9. College Allotment Letter.
10. Copy of fee receipt or receipt of security deposit. Apart from these keep your ID etc. with you.

https://www.shiksha.com/b-tech/resources/upsee-college-predictor
Go to the college predictor link I am sharing here to know about the college you can get.
Good luck.

Yes, but you have less chances (around 75% chances) that you can get admission into those colleges at this rank, because lateral entry depends on the basis of vacant seats available in the second year.

Hello Abhi.
Go through this link. This link will guide you to get the list of colleges for college prediction-
https://youtu.be/hOlit6Un7l0

It looks difficult but still, you can give it a try.