MBA Entrance Exam

Yes, you can try as the cutoff also varies yearly.

Yes, you can apply for CAT exam and your from a different field you will get extra points in the final selection after complete thing your GDP I rounds.

Yes sure why not

Few colleges that accept low CAT score are:
Jagannath international management school (JIMS)
Delhi school of business (DSB)
Doon bechne school Dehradun
New Delhi institute of management (NDIM)
Indian business school Hyderabad
IILM greater Noida
Asian business school Noida
IILM Gurgaon and Delhi
I hope this helps!
Cheers.

Their are many MBA colleges in Delhi, the best being
IIT Delhi
Amity University
Faculty of management studies.

You can apply separately to the college, but there would be a centralized counselling called CAP.

yes you can get admission in good colleges of all over India

Your profile is very nice. You should at least try for 90+ percentile. And it's quite simple thing the more percentile you achieve the chances to get into a top colleges is increased.

Yes, DTE Maharashtra will also consider GMAT/CMAT scores.

Yes. You might get a call for next round. You should try for 90+ percentile in cat then you will be in safe side. And in your case also if you get a call then you should try hard to convert your call into a seat. And there are other factors also which will impact on getting call like your education background your past experience etc.