Teacher

It depends on If you want to teach in schools or colleges or tutions/Coaching . There are seperate guidelines/requirements for each. But offcourse you atleast need to be a graduate to teach. Best of Luck !

You need to have atleast Masters or else preferably a PhD from reputed institutes of the country to Land into a teching job.
Yes IIT's could go well for you. Other than that you can consider good private colleges for your education too. You will have equal/Better oppertunities from there too.

Complete your graduation. Then M. Ed.

Hi
Jamia Milia islamia, Acharya nagarjuna, JNU etc are few universities. Rest you may check here:
https://arts.shiksha.com/government-sector-in-india-categorypage-9-37-1-0-0-1-1-2-0-none-1-0

You can join helloclass

Hi
You can start with maths hons and then go for master's with b.ed to teach in schools. If interested in professorship, take NET after m.sc.