I was watching I Am Become Death and when Maya (and her amazing changing accent) was cleaning up Mohinder's lab and then left all I could think was; where does Maya go when she's not at Mohinder's lab?

The obvious answer would be his apartment, but that would mean she does nothing in his apartment until she has to go to his lab for plot specific reasons.

It's not like she can get a job or anything, she's an illegal immigrant.

You already answered your own question...She hangs out at Mohinder's apartment.

Also, can't she get a fake green card in NYC?

Yeah I think she mostly stays at Mohinder's or walks around, shopping and things like that. She's spent months travelling over rough terrain to be there and ends up having nothing much to do. Must be disappointing, no matter how strongly she wants her life to be “normal.”

And she's a wanted mass murderess who‘s illegally in the country, so that’s another hindrance…

I wonder what happened to Ale, did they bury him?

That's a great question. It's not easy, at all. There been a few guides published which help newcomers to the city in finding places to go. But, off the cuff, I'd say she uses a port-a-potty no far down the street at a construction site. The workers there are too busy cat-calling to notice her mug on the "Mexico's most wanted" list.