NEET

Not sure about the government quota seat. Unless you have a reservation. But you can get management quota seat.

Vijay, to be eligible for NEET you should have studied Physics Chemistry Biology and English as your mandatory subjects. Now you can also study Biology as an additional subject and be eligible for NEET. So you should complete your 12th, pass in all subjects, take up Biology as an additional subject from NIOS and secure a minimum aggregate of 50% in Physics Chemistry and Biology. Now it is 50% for General Category, 45% for PWD and 40% for OBC, SC, ST. If you fulfil this criteria, you are eligible for NEET. If you like answer then Upvote it. Thank you.

You can start your preparation from the 9th only. NEET and AIIMS exams are usually conducted every year by MCI. They give us admission to various medical colleges in India. NEET syllabus covers mostly class 11th and 12th but both classes are somehow related to class 9th also. So, start solving MCQs based on your syllabus and give a mock test of NEET. Or you can join some coaching institute also if you want to.

You can refer to the cut-off page of VIMS through the following link: https://www.shiksha.com/college/vardhman-institute-of-medical-sciences-nalanda-64093/cutoff

Well, there is a very less chance but you can still try your luck. Don't be demotivated, you have secured a very good rank and you will definitely be able to get a seat in medical college next year if not this year.

Go through this link for the best books for NEET preparation. https://www.shiksha.com/medicine-health-sciences/articles/neet-preparation-tips-syllabus-and-best-books-blogId-22271.

If you have missed the chance, then there is no way to register now.

No, the NEET cut-off is not reduced for BDS.

All the rounds are over, you cannot apply now.

Yes, You can give the NEET exam while in your graduation. If you got selected and got a medical college then you just have to get a migration out of your B.Sc. Course and submit it to the medical college you get.
1st year B.Sc. Students have a awesome opportunity to score good marks in NEET as their knowledge about the exam is very new and their subject knowledge is also intact. They can easily clear the cutoff by proper preparation.