Science

BBA and B.Sc have not much difference. The main difference is always in fees and subjects offered.

Initially, you are eligible but admission is depends upon the meeting the DRC cutoff criteria. The eligibility criteria of B.Sc. (Hons.) Physics at DRC is as under.
Eligibility criteria: The overall percentage in PCM should be 55% and one compulsory language should be 50%.
Further the cutoff for B.Sc

Yes, that certificate is valid anywhere, so you can use it to pursue M.Sc or apply a job in Telangana.

If you encounter such a problem you should contact the respective college authoriy to sort the matter out. This is an internal problem and hence to take admission you should email them or call them up.

You should visit the website of MHRD, they have a plenty of seems for scholarship I hope there should be one for you too.

You can check out this link to get information about it https://www.shiksha.com/college/asb-amrita-school-of-engineering-bengaluru-sarjapur-road-bangalore-35737/courses/engineering-s
All the best.

Yes, you can get direct admission on the basis of class 12th without any entrance.
Good luck.