IIT

IIT BOMBAY
IIT Delhi
IIT KHARAGPUR
IIT KANPUR
IIT ROORKI
IIT MADRAS
IIT GUWAHATI
IIT HYDERABAD
IIT GANDHINAGAR
IIT BHU.

You may refer to the following link for tips on clearing JEE: https://www.shiksha.com/b-tech/exams/jee-mains/preparation-tips

Total seats in IITs are 11 (4 in IIT Powai and 7 in IIT Guwahati ) for B.Design for SC category students. You have lesser probability of getting admission in IITs for B.Design.

Check out the eligibility predictor for JEE Advance :
https://www.resonance.ac.in/answer-key-solutions/JEE-Main/2017/jee-main-2017-eligibility-predictor.php

Go through books of IIT-JEE books and previous year question papers.

If you are diploma candidates then you have to start your engineering with first year for IITs by qualifying the JEE Mains and Advance exam.

If you need to take admission in IIT, you need to qualify for JEE Mains paper 1.

To get into IITs only JEE exams should be cleared and if you are qualified you should appear for JEE Advanced and get a good score to get into premier IITs.
There is no need to apply for any other entrances to get into an IIT.
The official JEE main website is www.jeemain.nic.in

It is just great that you have thought to study B.Arch at IIT.
You should appear for JEE main paper 2 (B.Arch).
Almost all the coaching centers are good. I don't want to mention any coaching center names. If you want to get into any best institute then refer those which produced the toppers in JEE exams this year or the consecutive years.