CAT

Yes, you can. the last year's cut-off for IIM-A was 80%ile but for IIM-L, it was 90%ile.
Try your luck.
All the best.

The CAT cut off for IISC Bangalore is 99 percentile for MBA every year, as it is one of the finest college for MBA.

No, work experience is not mandatory to get admission in IIM. Yes, you can take CAT to pursue distance MBA.

Can you tell the error which is occuring?

Best Books for CAT by Arun Sharma (TMH Publications) or Quantum CAT
If you have study material from a coaching institute like IMS / TIME / CL, you should try to finish it from start to end. You should not even look at any other books.

Yes, there are many colleges affiliated to AKTU to pursue MBA like KIET, RKGIT, JSS, etc. They offer admission without CAT exam.

CAT is the most difficult exam which is conducted by IIMs. If you want to take admissions in the top colleges consider giving this exam, CMAT is the middle-level exam, you can go to some top colleges but not IIMs, MAT is the easiest of all the exams.

60-40, 60 for CAT/CMAT, 40 for GD-PI and your education background and work experience.

Yes, you can get via CAT score.

Hi Akash,
You have a good chance in getting calls from most of the top B schools such as IIMA, IIMB, IIMI, and FMS Delhi. Rest, based on your engineering stream, 10th 12th boards, and percentiles in individual components (VA, QA and DI LR), you can try predicting your colleges. For reference, the following link might come in use-https://www.shiksha.com/mba/resources/iim-call-predictor
Hope this helps.
All the best!