Interior Design

Yes, you can. Unless otherwise mentioned by the university.

While selecting the best institute, you need to check some of the important parameters such as recognition, year of establishment, batch size, syllabus, faculty, fees, placements etc. For your reference, here's a list of some renowned fashion design institutes in India:
National Institute of Fashion Technology
National Institute of Design
Lovely Professional University
National Institute Of Interior and Fashion Technology
Institute of Apparel Management
International School of Design
Indian Institute of Fashion Technology
LISAA School of Design

Yes, there are some courses. They provide in interior designing. You can apply for these courses.

Absolutely, you are eligible to do Diploma in interior designing.

It depends upon the institute you have chosen for the same. If they ask for the entrance then you have to give that.