Interview questions are not pass or fail. They are just there to gauge you're ability to problem solve and function under pressure. I hated interviewing, but disliked conducting an interview even more. The problem is people act so antagonistic when an interviewer challenges their ability, but realistically your character is whats really under scrutiny.

Having a great resume and stellar github is why you get the call back, an inability to conduct yourself in a professional manner is why you didn't get the offer. Especially in newyork, a medium post from an employee could affect stock prices, you can't have a lose cannon working for you.

I am sort of new to the whole startup scene. How much should I value equity if the company is only a year old?

Is there a formula or some better way I can gauge it's worth?

yes