No you can't but you can purchase a parking pass for the park they sell them at their office which is located in the park.
Federal passes don't apply to state, county or city parks. So, no.
I don't *think* so, but it's worth calling the office to ask. Street parking is free.
There is plenty of free parking on the street outside the park entrance
Parking used to be free many years ago. Don't know if it still is.
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