B.FTech

Yes, the National Institute of Fashion Technology in Kolkata offers a B.FTech education. At the UG Level, it also provides B.Des. At the PG level, MFM is available. Written exams are the basis for admission to all courses.
The instructors are also well educated and skilled in the subjects they teach.

Your rank should be within 1k, preferably below 500.

The only way to get in NIFT is by sitting for the entrance exam. There is no way of lateral entry.

Jamia Millia Islamia. YMCA University of Science and Technology. Indian Institute of Technology. Guru Gobind Singh Indraprastha University. Indraprastha Institute of Information Technology, Delhi. Fees of these colleges are very reasonable but u have to work soo hard for getting these colleges.

The fee structure at Dhruva College of Fashion Technology for Bachelor in Fashion Technology:
B.F.Tech - 2.1 Lakhs (1st Year Fees).

Score as much as you can. 100+ is the safe zone (myth: for getting top NIFT college like Delhi, Mumbai, Bangalore, Hyderabad etc. You need to get around 135+ ). Work hard before coming to NIFT and also work hard after coming to NIFT.

Yes there are college in Fashion design technology

Keeping the previous trends in consideration, the chances of getting B.FTech in NIFT are vary less.