Business Management Studies Eligibility

The cutoffs cannot be predicted as they accept CAT, MAT and TANCET. You would require minimum 80 percentile in CAT as per historical information.
You can check the below mentioned link:
https://www.shiksha.com/mba/course/master-business-administration-psg-institute-management/29681

The eligibility criteria of Ph.D at IGNOU is M.Phil degree/ a Masters degree in management discipline with minimum 55% (50 percent marks for SC/ ST/ PH candidates) or an equivalent grade from a university or a recognized institution of higher learning. After Ph.D from IGNOU, you are eligible for teaching job in B-schools and universities.

Yes, you are eligible, irrespective of your qualifications.

While MBA can be done with graduation from any stream, your subjects must be relevant to it and 48% is quite low. The best way is to get admission into a diploma first and once you clear it, you can go for a degree. Check imperial college - Australia and feel free to revert.

MDI is rated among the top 10 MBA institutes. Its admission is based on performance at CAT (open test). You need to ensure that you get more that 90 percentile to seek admission in it

Yes, after completion of the course or in the final year you are eligible to write NET exam. Until then just wait and prepare.
All the best.