Are the lights on to the basketball courts all night into the early morning?

They actually stay on until 10-11 pm. They are not motion activated. There is a button you must push for them to come.

They are not. The park closes at 10 p.m. each night.

No

As far as I know, they're motion activated but they turn off randomly and dont stay on past 12.

No they turn off around 9 pm