Degree

Yes, you are eligible. If you have filled entrance exam form last month, you can give the upcoming exam for 17000 vacancies.
All the best.

1. University of south California.
2. University of wisconsin milwaukee
3. Ohio State University
4. Temple university
5. University of kansas
These are the best colleges offering graduation degree in hospital administration.

Hi, you should confirm this with the concerned authorities once for clarification because it depends on them how much leniency they give you for the following case. Else, you can ask your college for the degree mark list, telling them that the one you had is misplaced. Hope it helps.

Yes, you can get admission in Karnataka or another state through lateral entry.

Yes, you can do your degree after your Diploma, but you need to pass 10 +2 to enter graduation study which you can't do on diploma certificate at least not in Karnataka.

Goa Institute of Management, IIHMR, Tapmi, Symbiosis.

Your profile is very good. You will require following things to apply an American university for undergraduate degree:
1) SAT, SAT subject test and TOEFL score
2) Two teacher's recommendation
3) One counselor recommendation
4) Your 9-12 grade marks
5) Your personal essay
6) Extracurricular activities which you have already mentioned. Feel free to ask questions.