India

There are many wonderful universities in London that you can choose. I am still willing to write an answer to this even after seeing the timeline when the question was posted. The reason is I have a friend who studied in the UK and was placed in a very good company. Do get good grades and get admission in one of the best universities in the UK.

Please mention the course you want to enrol into Anna University for better assistance.
To check eligibility, follow the link below and look out the for the desired course for exact results:
https://www.shiksha.com/university/anna-university-Chennai-3084

You may have to check if you can practise medicine in UK and if your certificates are valid in UK. If you wish then you can even study a year or two or more which will make it easy for you to establish a business and settle. But validation of any course that you have done is very important.

Go the websites given below you will get cut-offs and all other information regarding NCHMCT JEE:
https://www.shiksha.com/hospitality-travel/hotel-hospitality-management/exams/nchmct-jee/cutoff

Music Colleges in Rajasthan-
Ajmer Music College, Banasthali Vidyapith Faculty of Fine Art, JaiNarain Vyas University Faculty of Arts and Social AND SCIENCES have good reviews.

There are over 24 MBA in Healthcare & Hospital colleges in Delhi/NCR. Please refer to the link provided below for a detailed list of these colleges. You should be able to navigate to some of the better colleges on this list using the filters on the web page. Regards. https://www.shiksha.com/mba/colleges/mba-in-healthcare-hospital-colleges-delhi-ncr.

https://www.shiksha.com/mba/ranking/top-mba-colleges-in-Karnataka/2-2-106-0-0
Kindly refer to the above link for top MBA colleges in Karnataka ranked by Ministry of Human Resources and Development.

Top Engineering Colleges in Hyderabad Accepting AP EAMCET are mentioned at the link provided below. The ranking is based on rankings published by India Today, The Week, and National Insitute Ranking Framework (MHRD).
https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-hyderabad-accepting-ap-eamcet/44-2-0-702-6490

Yes, there are students from different states pursuing MBA.