Is the parking lot owned by the state or privately owned? I am asking because military can park for free at state and city owned lots.

They are owned by the park. Since there are stops before the park entrance they installed parking machines to sort of pay for the park entrance at those parking before the entrance and others inside if no personnel at gate

Yes, tolls along the way! But parking machines have been added in some areas! You have to pay the machine to park in some area's! But as far as who owns, I would say the state, but I'm not 100 percent sure!

You pass through till booths and gates to get in; it's not a pay to park lot.