Colleges in Karnataka

Manipal is a different experience but for BBA I would suggest you to try for DU.

Yes, you can join. There are many opportunities post MBA and since you also have work ex chances of good placements are high.

You can go for these-
Jain University
MS Ramaiah
Acharya Institutes

Yes, you can get admission.

Acharya institute of technology will be a better choice.

I really don't think so. They offer scholarships the details of which you can find in the link given below: https://www.jainuniversity.ac.in/Scholarships-offered-in-India.php

Admission is through counseling based on the rank obtained in Karnataka Common Entrance Test (KCET)/ Consortium of Medical, Engineering and Dental Colleges of Karnataka Under Graduate Entrance Test (COMEDK-UGET).
Candidates taking admission under management quota and international quota can directly apply to the institute. Regards.