Dance

Yes, you can apply for M.A. in Dance at Rabindra Bharati University - RBU.
The minimum eligibility criteria for admission in this college is that the student must have passed 10+2 examination with special aptitude in dance.

If you believe in yourself that you can score good in NEET/AIIMS exam in the next attempt, then you can take a year drop. Also, ask yourself whether you want to become this or not. Ask yourself whether dance is your hobby or passion. If passion, you should practice hard and give your best in it. Don't live a life in which you can't be happy. Think what you want and then take a decision.

There is no college in Bhopal which provide degree in Kathak. For further information visit
https://www.shiksha.com/arts-fine-visual-performing/dance-choreography/colleges/kathak-colleges-india
Hope it helps you well.

You also have other ways of starting a career in this, as you can also start to teach students by opening your own classes. this will also allow you flexibility in timings and would be like a part time job

Yes you can. Candidate must have passed 10+2 or its equivalent with special aptitude in dance to get admission in this college.

It's not compulsory that you have to take arts to get admission here. The minimum requirement for admission is 45%(40% if you are from reserved category) in any stream from a recognized board. The admission is based on the entrance exam.
Please refer to the link given below for more details:
https://www.shiksha.com/arts-fine-visual-performing/dance-choreography/course/b-a-in-dance-savitribai-phule-pune-university-ganeshkhind-274337

No, it does not matter.