Bangalore

The top most college is IIM-B. You can also opt for XIME, Christ College or Alliance.

Both of these colleges are good. You can check their websites for information related to their placement.

Yes, IBS, Hyderabad, and Bangalore are good options to pursue MBA. IBSAT is a little bit easy to qualify than CAT.

Hello,
Yes, definitely. Bank PO job is good for everyone
But yes, there are high work responsibilities on PO. Any graduate student can apply for Bank PO exam and the competition is really tough in it.
Checkout the complete preparation plan here - http://www.slideshare.net/PriyankaGupta1234567/ibps-bank-po-study-plan-the-perfect-strategy-to-crack-ibps-po
I hope it will help you.
Best of luck.

Only admission committee can get you the exact details. Such confidential information cannot be shared on the internet. Better you ask them out.

Such specialisation is not offered. You can Do MBA in Supply Chain for such roles.
https://www.shiksha.com/mba/colleges/mba-in-logistics-management-colleges-in-bangalore

You should opt for SJBIT. SJBIT is doing well and its placement assistance is good too. You can get good salary package after completing your MBA from SJBIT.