MBA/PGDM

Keep IIMs as top priorities and write CAT for them. Apart from them SP Jain, BITS Pilani, Symbiosis, XLRI and Faculty of Management Studies are good choices.

Yes, you can apply.

IMT - Navi Mumbai and Bharti Vidyapeeth will be the better option for you.

You can apply in MICA.

That's not exactly true. It is just a rumour as of now.

Both are good options for a better career. If you have been graduated from commerce stream, then finance is a good option. If you are from BBA or Bachelor's in a subject based on marketing, then you must go for marketing.
Marketing needs more of analytical and reasoning skills, generally people start

You can opt for Symbiosis distance learning to pursue MBA. You can also opt for IGNOU.

For reputed B-Schools, CAT cut off is around 80 percentile. Well, it depends on individuals choice which colleges they are considering, and the percentile they have scored in CAT.
IIMs generally have cut off >96 percentile.
MDI-Gurgaon, SP Jain, NMIMS-Mumbai, JBIMS, FMS, IIT-B/D have cut off above 95

MBA intake is approximately 750.