Yes you can write GRE exam/GMAT exam for MBA. It depends on the colleges abroad as what their admission criteria is.

The eligibility to study from a commerce background also depends upon the college you are interested to study abroad.

There is no specific eligibility for GRE and is given

Yes, you can definitely get into Pune University for an MBA if you are a non maharashtrian student. For that you will have to appear for MHCET. The cutoff is around 85 percentile.

The university is accredited grade “A” by NAAC.The University imparts professional /non-professional education, research and training. Only candidates with the relevant qualification can register for these programmes. Seats are reserved for people belonging to different categories such as SC/ST/BC etc. as well as special categories viz. Differently-abled etc. in accordance

Here you do not mention any college name or which college you want to know so I give you some to top college name and their fee structure hope this is helpful for you.
Generally, the MBA course fee in India presents an extensive range – it may range anywhere

Yes, you can appear for MH CET MBA if you are in your final year of graduation.

There is no age bar to apply for MH CET MBA. 

To know complete eligibility criteria of the exam you can refer below link

MAH CET Eligibility Criteria 

Good Luck!!

Please explain the college for which you want to know the colleges accordingly I can help you.

You can check the list of top colleges for MBA below

Government

Indian Institute of Management Ahmedabad

Indian Institute of Management Bangalore

Indian Institute of Management Calcutta

Indian Institute of Management Lucknow

Indian Institute of Management Indore

Private

XLRI – Xavier School of Management, Jamshedpur

Management Development Institute, Gurgaon

SPJIMR,

For doing Masters in Banking and Finance, you can choose colleges in Delhi like New Delhi Institute of MAnagement or Jagannath Institute of Management Studies. In NDIM, companies like Deloitte, Capital Trust, Yes Bank, Axis Bank and many more offers you good packages.

Based on your score you can expect new IIMs & other colleges like Xavier Institute of Social Service, Ranchi, We School, Bangalore, MS Ramaiah Institute of Management, Bangalore etc. You can check your other chances with CAT Pathfinder Tool.

CAT Pathfinder Tool

Good Luck!