Fashion Design

Yes, you can take. You can purse B.Tech in Fashion designing after 3 years diploma in garment technology. The eligibility of B.tech in Fashion designing is to qualify the diploma with a minimum of 45% aggregate marks and you should qualify the ECET entrance exam .
Other way of getting admission is to go through management quota

You can see eligibility and other admission details here https://www.shiksha.com/college/national-institute-of-fashion-technology-chennai-taramani-27353/admission#admission

Yes, you can do. NIFT and LPU are the Institutes offers B. Des in Fashion Design course. The eligibility criteria are as under. Eligibility Criteria for LPU (Qualifying Exam) :- Pass with 50% aggregate marks in Diploma (Fashion or Garment Technology) [ (3 years after 10th) or (1year /2 years after 12th)] or equivalent, subject to qualifying LPU-NEST. Eligibility criteria for NIFT :- 3 or 4-years Diploma recognized by AICTE or a State Board of Technical Education.

There is no such entrance exam to get admission in the JD Institute of Fashion Designing. Candidate must have passed 10+2 from a recognized board to get eligible for the course.

Admission process for 2019 session is closed now for fresh admission , you can apply for 2020 session in October, 2019 by logging in to https://nift.ac.in/admissions

Yes, Diploma in fashion designing is a 3 years course just as most of the Diploma courses are of 3 years.