Hospitality Management

Yes, sure, you can choose a college outside of Delhi of your choice. You can go outside of Delhi like Jaipur, Shillong, Shimla and so on.

Entrance exams are conducted for hospitality courses by many universities and colleges.
NCHMCT JEE:
Army Institute of Hotel Management& Catering Technology (AIHMCT)
Bharati Vidyapeeth Institute of Hotel Management and Catering Technology BVP CET HM) 2019. Common Hotel Admission Test by IIHM (e-CHAT)
Guru Nanak Institute of Hotel Management Joint Entrance Test GNIHM JET 2019

I would suggest go for B.Sc. Since it's offered at some of the most prominent institutes in India.

Yes, you are eligible to go for higher studies in Australia. You should complete your class 12th board first. And remember you should not have any compartment or pending backlogs. Best of luck.

Hello,
Kindly go through Shiksha link for information about hospitality management.
https://www.shiksha.com/hospitality-travel/hotel-hospitality-management/course/b-a-in-hospitality-management-iam-institute-of-hotel-management-guwahati-151509

https://www.shiksha.com/college/siitam-sun-international-institute-of-tourism-and-management-Hyderabad-Ramnagar-33259
Use the link to know about the same.
Good luck.

It would depend on the colleges you have given preference for. If the specific college has high demand then you would have to go for repeated counseling session.