National Institute of Fashion Technology, Patna

No, as a matter of fact find ways to use your background. Being a science student will help with entrance exams. Try to keep up with the latest news and find ways to work on your design/sketching skills. Make a list of all the deadlines for the college's you want to apply to make sure you don't miss them.

Yes, you can either do a fashion designing Diploma or a certificate course. If you have or when you get enough technical experience you can start doing Internships to get experience/make contacts. Find local colleges around you so you can hit the ground running.

Seems highly unlikely with this rank. However, you can try for NRI admissions.

Yes, they do offer hostel facilities.
https://www.nift.ac.in/mumbai/Hostels

This depends on what course/campus you want to apply to. However, it seems difficult with this rank.