I understand the parking lot closes at 6pm and cars must vacate by 8pm I believe however does the beach remain open if we park somewhere else or take an uber from a parking area a few miles away? Can you remain on the beach into the night?

The whole park closes at 8:00 PM, and you must leave by then.

No, the Park Rangers will patrol past closing and move everyone out. See below for the time info... Summer Hours (Starts When Daylight Savings Time Begins): Park open daily at 6:00 AM. Entrance stations are open daily until 7:00 PM. Vehicles may enter the park until the inbound gates are closed at 7:20 PM. All park operations and gates close at 8:00 PM daily.