Colleges in Kolkata

All the colleges have their admissions going on right now and for BBA the top colleges according to me are:
1. St. Xavier's College
2. JD Birla Institute
3. ILEAD
4. Amity University and many others are there.

I think you will not get Heritage and IEM with this rank. Techno you will get some of the branches. Try for other colleges I am attaching the link where you can check all the details:
https://wbjeeb.nic.in/wbjeebcouns/orcr/PrevYearORCR.aspx.

Yes, placements are there after BBA but to get good salary packages go for MBA after BBA.

Refer the following link:
https://www.shiksha.com/b-tech/resources/wbjee-college-predictor

Amity University, Gwalior is a private university located in Madhya Pradesh. It is accredited Grade A by the NAAC. Amity Gwalior offers B.Tech course in total 9 specializations. The candidates who are willing to apply for this course must have scored at least 60% in Chemistry, Math, Physics, and English combined in 10+2.
The eligible candidates can apply for Amity JEE exam. The selection of the candidate would be done on the basis of the score obtained by the candidate. The will followed by a test on the day of the interview.
Direct admission is also done on the basis of a valid score in JEE Main.

https://www.shiksha.com/b-tech/course/b-tech-in-bio-technology-techno-india-university-salt-lake-city-kolkata-200973
Refer the above mentioned link.

No, you won't get CSE in Heritage. Try for other branches.