Exam

No, your rank does not satisfy the cutoff criteria required to get into CBIT. You may get into CBIT if Reservation is concerned.

Since you have not mentioned your university, it is quite difficult to say. But, in general, it sure does seem possible. A lot depends on the marks of people around you (as IIM Bangalore grades your marks relative to others and then gives your application some points). Anyway, it does seem possible,

I will be honest that IIM Bangalore is going to be very difficult for you. But, you can target IIM C, they give very low weightage to graduation marks.

There are many other engineering entrance exams, you need to prepare for those exams and try to crack them to pursue engineering in private colleges like SRM, GITAM, etc.

Yes, college like DU, Christ University, Symbiosis, IP University and many colleges conducts Entrance exam. BMS is offered by DU and Xaviers college Mumbai and Xavier college, Kolkata takes Entrance for BBA. These are best college for BBA and BMS.

The chances of a non local getting a seat are less, but you may even attempt TS EAMCET for better chances for getting into CBIT. You need to get a good rank to ensure a free seat.

Refer college rankings of reputed magazines. I got into Doon Business School, Dehradun last year with 93.5 % in CAT.

Hello Animesh,
For any entrance examination, you can only choose any one mode of examination either offline of online, if you fail to give offline examination it can be converted into online. So, look forward for next year.
All the best.

There are many other engineering entrance exams, you need to prepare for those exams and try to crack them to pursue engineering.