CAT

First complete your BBA then prepare and give CAT and get admission into IIMs.

Sometimes they do overlook these marks if you have performed well in other areas. Do prepare well for CAT prepare for the interviews and you might expect a call from IIMs.

Aggregate marks till that semester can be considered.

You can refer to the link given below-
https://www.shiksha.com/mba/colleges/mba-in-supply-chain-colleges-india

Yes are can eligible for CAT exam.

No. You need to take up TANCET to apply for MBA at Anna University. They only accept TANCET scores.

You should show B.Com in your graduation degree as that is a mandatory field.

https://www.shiksha.com/university/uoh-university-of-hyderabad-23069
You will find all the true and authentic information about the cutoff here.

You are effectively competing against fellow fresh graduates for the seats. In any case, you have most likely to do better than an average experienced candidate in the CAT exam and that should count for something. If you have one or two years of work experience, this is not a game-changer.