Diploma

Before I suggest you the best hotel management colleges in India, I would like to throw some light on the fact that you must look out for the best courses that match the current industry standards and have adapted to the changing trends. Thus, courses in hospitality, travel and tourism will help you get a wide array of career opportunities.
Here are few options for you :
IHMs all over India
Oberai Centre for Learning and Development , Delhi
Army Institute of hotel management and catering technology, Bangalore
UTM, Shillong

The first and basic qualification required for a Ph.D course is that you must have completed your Masters degree course.
To apply for Ph.D. you can either directly apply to the professors of different universities sending them your resume, Statement of purpose
and your research papers. Or you can appear for UGC-NET examination.
And then, sending your NET scores to the professors under whom you want to undergo your Ph.D course.

Yes, you most definitely can pursue a course in B.Sc. (Interior designing) after completing a diploma in interior designing.

Yes you can get admission by giving NATA entrance exam.