Delhi

Hello dear,
If you want to get admitted into NSIT then you must have appeared for JEE Mains and secure a good rank in JEE Mains too. After getting a good rank in JEE Mains, you have to fill a separate form for counselling JAC Delhi. In order to take admission in NSIT, you have to appear for JEE Mains then you have to participate in JAC Counselling. This year cut-off rank for All India level is 4867. You need to score above 60% aggregate in PCM.

https://www.shiksha.com/design/fashion-design/colleges/colleges-Delhi-ncr
Kindly visit this link.

Delhi Technological University
Bharati Vidyapeeth's College of Engineering
Dr. Akhilesh Das Gupta Institute of Technology and Management (Northern India Engineering College), Department of Computer Science
Maharaja Agrasen Institute of Technology
IIT-D, Department of Computer Science and Engineering
Maharaja Surajmal Group of Institutions
Ch. Brahm Prakash Government Engineering College.

You can check out the options given in the link https://www.shiksha.com/science/colleges/b-sc-biotechnology-colleges-delhi-ncr. This link contains list of all the private college in Delhi and Noida for your desired subject.

There are fairly high chances that you can get NIFT, Delhi.
Check last merit rank admitted in 2017 at http://nift.ac.in
The difference in domicile and general is that if there is any NIFT center in your city, then you will get a little advantage of that under OBC domicile.

No, it is not possible, if you don't have any reservations.