Does tag of college (IIT/NIT) matter in the job market especially for girls?

Yes, HRs aren't competent in tech, so they use the tag as a proxy.

But that shouldn't stop you, it doesn't mean it's the end of the road for you. It doesn't even matter if you have a good experience or are undeniably competent.

Nope I am passed out from tier 3 college where even tcs infosys not visit for hiring having 48+ backlogs in final year earning more than 30+ lpa as sde in unicorn startup although i have completed my degree in 8th year of education but college is not matter now working with BITSian, IITian, NITian etc

Why do you think it is different for girls

It gets your foot in the door but rest is upto your skill. Definitely opens more doors

In India. Definitely yes. Even if you absolutely unskilled piece of shit, but can fake like you know everything and have the IIT tag, companies are ready to throw minimum 20L at you

Short Answer - Yes it does matter! Lets say you are X from a Tier 3 college and there is another person Y who has exactly same skill and experience but is from a Tier 1/2 college. In the screening round itself they will prefer Y. Have experienced this first hand with a lot of reputed companies and have screenshots of HRs rejecting my resume based off my college. But that being said, it shouldn’t be an issue as there are enough companies and enough job opportunities in the market. But yes it reduces the scope/targets of getting chance to get interviewed by companies in the market. Again in this case lets say both X and Y apply for 10 job opportunities for same position. Y might get interview calls from 7-8 companies whereas you would get only 4-5 interview calls so the scope for you kind of shortens in terms of opportunities.
Rest is all upto your hardwork

Yes and Yes

It matters for getting short listed for interviews, not so much after that.

In India yes (limited to the screening stage)... it's pedigree.

In India, a lot