MBA/PGDM

I don't think Sinhgad offers any concession. For more details, you should contact the college.

Yes, you can definitely pursue MBA from Australia, but you need to have a proper justification for the year gap. However, your profile looks good, the gap factor should not be a problem.
All the best.

MBA is a better option as MBA is a degree course while PGDM is a Diploma course. Although, both are treated equivalent but in most of the PSUs and MNCs, degree course is given more importance.

Yes, definitely, you can.

Yes, you will get a form as well to fill before WAT/ PI and they will inform you about the dates and slots, accordingly. Yes, IIM - Raipur in the recent years have made the mark and it is one of the best option to pursue MBA.
All the best.

I don’t think there are many colleges under CMAT and MAT for MBA IB. You can appear for CAT exam to pursue MBA IB.

Pune University is a better option because it has good placement records and good reviews about faculty than XISS. XISS is also good, but the main focus is on social service course.

Hi,
To get admission in the best MBA institutes/ universities, you need to appear for an entrance exam like CAT, MAT etc. If you want to join 2017-2019 batch, you can still appear for May MAT exam. Else, you will have to wait another one year to qualify for CAT, XAT or CMAT.
All the best.