PGPM

Sorry if you want a regular MBA you need to write CAT. Also you have another option of taking executive MBA from IIMs.For that there is no CAT barrier.

PGDM, as the name suggests, is a diploma and not a regular degree. Its syllabus focuses on practical aspects of management and is very concise.
MBA is a regular Masters degree with benefits of both, being superior to diploma and being a PG course. Its course is also very elaborate. Hence, more merits mean more fee. Also, MBA students are placed more easily than PGDM.

No, only MS degree for full-time MBA course.

You will need a percentile of 90.78% in the CAT exam to apply to this colleges for Post Graduate Program in Management. Regards.

There are some companies which come in for international placements in countries like Dubai, south African, etc. There is a process which is followed for international placements which is disclosed to the candidates who are applying to the concerned company.

Kindly visit the link mentioned below:
https://ask.shiksha.com/is-ibs-mumbai-aicte-approved-and-recognised-by-ugc-qna-3451213

At IBS or WeSchool, if you want to do Marketing, then it's fine. But healthcare at Welingkar is just a new course and we can't predict it's scenario at this level. Adding to this, internships we're good in health care as people got placed in health care companies. So, We-School is also a good option as it gives freedom to chose your specialisation also within Healthcare.
All the best!