Hello!

1) To have a valid recognised post graduation, as the institutes are autonomous, the PGDM course should be AICTE approved. But secifically to make PGDM equalivalent to MBA the course should be AIU approved. You can only pursue PHD only if your PGDM is AIU approved.

2) Yes, you're eligible to appear for UGC NET or SET. They accept PGDM.

I hope this helps.