Yes You have to pass a background check.
You can find all the details about the background check and Driver/Vehicle requirements in this link:
Yes. They will notify you in as long as two weeks, letting know if you qualify as a postmate.
Yes I have to pass the the background.
Yes. But i passed, and I'm on felony probation and have 2 felony convictions in the last 3 years. (Non violent)