Arts ( Fine / Visual / Performing )

Well, I can only say that Masters is always better than Bachelors as it gives a deeper knowledge.

IGNOU is your best option for Distance learning in any UG or PG course. More details abouy the programme can be found below
http://ignou.ac.in/ignou/aboutignou/school/sopva/introduction.

St. Xavier offers Bachelor of Arts. They do not have the fine arts course.
Refer the link to know about the courses offered.
Link: https://www.shiksha.com/college/st-xavier-s-college-mahapalika-marg-mumbai-1184/courses?bc[]=1&ct[]=151&lo[]=1153

You must have passed 10+2 or equivalent with special aptitude in dance.

Yes, you can get admission. I would suggest you to go for a full-time course for better career prospects in future.

Refer to the link below to know about the colleges:
https://www.shiksha.com/humanities-social-sciences/colleges/b-a-colleges-delhi-ncr

Please mention the name of the course which you wish to pursue.

After 12th with arts you can go for courses like BBA and other similar courses such as BBM and BMS which open doors to numerous branches of management. Some of the most common specialisations one can seek to include Human Resources Management (HRM), Retail Management, Finance Management, Sales and Marketing Management, Logistics, Operations and Supply Chain Management, etc. You can also go for fashion designing, textile designing, Animation, hospitality and any other course depending on the field you wish to make your career in.

There is no course as FSP in JNU Fine Arts College. The course offered is B.Tech Facilities & Services Planning. To know about the details refer:
https://www.jnafau.ac.in/courses/b-tech-facilities-services-planning/