Can you park before you check in, i.e. can we leave the car there early in the morning and return after 1 pm to set up camp?

You can park in the parking lot to the right of the check-in building. You'll have to ask or call someone inside the check-in building about how long you can park in the lot.

I would think so. There is a big parking lot to the right of the check in building.

There is a small parking lot at the entrance that people park to check in. Otherwise, there is a pay station that you can use to purchase parking for use in the park.