Hospitality Management

Yes, it is quite possible.
The eligibility depends on the type of course that you wish to pursue, the details of some courses is stated below:
Diploma Class 10th pass from a recognised board with minimum 40% marks.
Bachelors Degree: Class 10+2 examination with at least 50% marks.
Post-graduation degree: Bachelors degree from a recognised university with at least 45% marks.
Graduate & PG programs may also require you to appear in entrance exams such as NCHMCT, AIMA UGAT, E-CHAT etc.

Garden City University one of the highly equipped college with experienced faculties from the Hospitality Industry. I'm a student of Garden City University of 2nd year. If I need to suggest it is this college which has 100% placement records.

Dear Rajiv,
This course has a vast options.
Travel Agencies and Tour Operations
Airlines
Hotels
Destination Marketing Companies
Event Management Companies
Government Tourism Boards
Travel Related Services
Travel Implants
Guest Relations teams of various reputed companies.
some career options are these. If you want to look out of the book then you could be an entrepreneur in this Tourism Industry. It's one of the revenue making industry.

Yes, definitely,
There are colleges which offer Travel and Tourism specialisation. Its one of the best industry and you can just complete your 12th and join this course. In Garden City University we have a course for Tourism and it's BA in tourism (Hons). Please check the website www.gardencity.university It's one of the top universities and the best course and training is given here.

There is no compulsion as such. You can pursue any course in Masters.

Basically, it completely lies on your interest.
For Bcom graduate, Finance is a good option to go for.
I would suggest you to go for top collegs itself, like IIMA, B, C, L, K, JBIMS, Sydeham, etc.
Kindly check the list at below link:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india/2-2-0-0-0