If you're going to leave it overnight, I would leave it in the top section. Also, this isn't a national park. It is a national forest.
You can if you have the daily or annual pass.
My understanding is that for national parks, you need to get a hiking pass and then you can leave your car parked overnight.
I believe you can. I would call local ranger station or state park. I personally didn't camp but when I hiked did see campers there.
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