Colleges in Bangalore

There is no minimum score as such (B has >80% criteria, might have changed so do check)
Put in your best effort for CAT, all this comes later, and you anyway can't change your scores.

Yes, but you need to perform well in GD-PI too.

IIM-Bangalore has some strict percentage criteria for boards (80% above in 10th and 12th, if I am not wrong). So, B might be off the books, but you still seem to have a decent chance at C with a high percentile. I don't want to be blunt, but you will really need to nail CAT hard. Otherwise, try looking at ISB, etc. wherein the admission isn't so marks based.
Good luck.

Jain University is preferably good. You should go with this option.

Which group did you opt for in class 12th, PCM or PCB?

Yes u will surely get a good college like Dayanand Sagar college,Etc.

BBA in Christ University is ranked number 1 at all India level.
Comparing it to other courses that too of other colleges will not be apt.

There is no need to send your marks sheet to apply in this university. It has an interview procedure.
If at all any of the programs require you to submit your documents, you can send the via post addressing IPM of the university.

According to MHRD NIRF 2017 ranking, VIT is better.