NCHMCT JEE

You need to attend the counseling in the final round of seat allotments and if you are lucky you will get the seat.

If you are from general category then it's not possible. Last year's closing was at 4198 for general category.

Yes, you can. But, for that you need to attend all the 3 counseling rounds, because your rank is a little low, but you can be lucky in any of the counseling.

It is difficult to get the seat for you because of your rank but any chance that you have IHM Hyderabad is that you need to attend all the counseling where the last round the institution who have vacant seats are provided to the students. But really tough for you so should change your institution choice.

Yes, there is possibly in second round. You attend all the rounds. Please check the cutoffs of 2017. Last year, it got closed around 10000. Again, there are separate sears for vegetarian courses. www.nchmctjeecutoff2017.

Yes, you can get the seat, but make sure, if you don't get the seats, you attend all the counseling with the final seat allotment, where can you easily get a seat in any of IHM. As your rank is good, you will get the seat surely.

https://googleweblight.com/i?u=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&grqid=y3EjC5gU&s=1&hl=en-IN&geid=1031
Please, go to the college predictor link I am sharing here to know about the college you can get. Good luck.

Yes, you can give NCHMCT JEE next year but for that you need to prepare well.

IHM Mumbai would be a hard shot for you. But here are a few other IHMs equally good:
IHM Bhopal
IHM Bhubaneswar
AIHM Chandigarh
IHM Chennai
IHM Gandhi Nagar
IHM Goa
IHM Hyderabad
IHM Jaipur

There are a few IHMs you can get. But admissions also depend on your reservation status.