NEET

We'll the cut off for this year is very high
There is no possibility of getting a government seat through All India quota, unless you have any category applied. If you belong to any non competitive states like Jharkhand, west Bengal, Odisha etc. , you may get seat through state quota. If you have any reservation you can surely get seat in some part of the country. Or else it is quite hard. If you are GM then there no possibility through All India Quota.

According to the information you have given you may get these colleges for MBBS course. A list of MBBS colleges in Maharashtra is
1- MGM Medical College, Navi Mumbai.
2- Bharati Vidyapeeth DU Medical College And Hospital, Sangli.
3- MGM Medical College and Hospital, Aurangabad.
4- Data Meghe Institute of Medical Sciences, Wardha.
5- Dr. D. Y. Patil Medical College, Hospital and Research Centre, Pimpri, Pune.
6- Data Meghe Medical College, Nagpur. For more details, you may use the Shiksha MBBS college predictor. (https://www.shiksha.com/medicine-and-health-sciences/neet-college-predictor). I hope this will help you.

If you don't belong to reserve category like ST, PH, then you can't get a seat in NEET UG.

No you can't get a seat this year. Try harder next year.

You can get seat in your state college only. You rank is a little bit low.

Yes, you can participate in AIQ counselling for free seat if, you can bear the fee you can apply through the Meghalaya state quota seat must be allotted on merit base and reservation based.

Sorry, but your score to get admission in government medical college is quiet low. However, you can try other courses like Physiotherapy occupation therapy B.A. MS and BHMS etc. In these courses you will get admission surely!

Your expected Rank based on your score will be ranging from 35900-36400. You have less chances in 15 % quota seats, but you can try in state level colleges. Chances of government college can be in state colleges. Good Luck.

These are the Colleges you can get in to with your rank of 391610
Government Sivagangai Medical College and Hospital
Government Thiruvarur Medical College
Shree Bhausaheb Hire government Medical College
Government Sivagangai Medical College and Hospital
Dr. Ram Manohar Lohia Inst. Of Medical Sciences
Pandit Jawahar Lal Nehru Government Medical College
Vasantrao Naik Government Medical College
Shyam Shah Medical College, REwa
Government Medical College, MIRAJ
Government Medical College, Barmer.