2 part question

This is a 2-parter:

1) I know the Quincy Center T stop has overnight parking, but I was wondering if there was a limit on when you could get in? I have an early flight on Friday morning, and am taking a cab from Quincy Center, but some friends need a place to park, and we need to leave Quincy ~4:30am (ie, before the trains and buses start running).

2) There's a cab stand behind the T station, but again, I doubt cabs will be there at 4:30am...anyone know for sure?

Thanks in advance! I tried Googling, but could only find rate info...