Does the greyhound bus station remain open all night.

Yes 7days a week including holidays 12am to 11:59pm sometimes you gotta walk around to another door. they close doors when there is less traffic for security reasons.

Yes

It says it is open but it was not open when I went to pick someone up. They waited outside in the pooring rain. There is an overhang though.

Open from 12am to 11.59pm