Colleges in Mumbai

Yes, you have a fair chance of getting a GD-PI call. There are a lot of students every year who perform well in GD-PI and convert despite their low score in entrance exams.
Good Luck

For MMS program, you have to go through the CAP process and the process has a major weight to the CET exam. But for PGDM, you have a fair chance of conversion but your selection will depend on your performance in GD PI.
Good Luck.

The Diploma Certificate course offered by institutes like Arena, MAAC, Framebox etc. Don't look at your grades. But, universities that offer a full time degree might. So, if your interest is to join the university, try them first and if you get admission then all good. If you don't get admission try doing a degree equivalent course in one of the above mentioned institutes.

Yes, you are eligible. The minimum marks requires in class 10th for Diploma engineering programmes is 35% in aggregate. Further, the admission are done through the common admission process (CAP) conducted by DTE Maharashtra. Hence, participate in CAP round for admission.

You can refer the link below for colleges offering PGDM course
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-Mumbai-all/2-2-0-10224-0.

You need to attend for jee mains for barch examination paper.

Yes, definitely every column need to fill before appearing for admission.