Exam

It doesn't accept CMAT but only accepts CAT with 86 percentile and XAT with 80 percentile:
https://www.shiksha.com/mba/course/post-graduate-diploma-in-management-loyola-institute-of-business-administration-nungambakkam-Chennai-187300.

Yes, chances are good enough. For top colleges under CMAT you can refer below in case you don't get it at above Institute:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india/2-2-0-0-0.

For top colleges, eligibility and cut-offs, see the link shared below:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india/2-2-0-0-0.

Mumbai is the best and Bangalore is the second best. Have a look:
https://www.shiksha.com/bba/course/b-b-a-nmims-anil-surendra-modi-school-of-commerce-vile-parle-west-Mumbai-130133.

Location is majorly metro cities like Mumbai dekhi Kolkata and also Bangalore, Gurgaon. TIME and CPLC are top notch with best conversion record following by CL

CAT and CMAT's cut-off is mentioned below for all colleges. So, you can match your score accordingly:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india/2-2-0-0-0.

More than 70 Percentile shall be must. Cut-off varies every year and the range is based on historical data:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india/2-2-0-0-0.

Minimum 3 months for crash course and maximum One year for long-term programme. Top MBA coll mentioned below:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india/2-2-0-0-0.

MBA education like the distance education, online education, part time which do not require any entrance but that will not be any good. As I can see lot of suggestion for entrance and that's true. If you want to pursue career in management then for sure go for entrance and do the regular education. I would suggest one of the best of Jaipur I. e. university of engineering and management that will do your job.

For PGDM, chances are good, but for MS cut-off is way higher. For details about colleges list and eligibility check the below-mentioned link:
https://www.shiksha.com/mba/exams/mah-cet.