No, there is a fee for all campsites.
No, it is a state park. Try BLM land ,but none close by. You can also boondock in certain areas on National park land.
You can tent camp for free at the park-and-pack sites... but its first-come-first-served - you just have to register at the forest service center. The sites are spread out and you have to pack your gear in (1-4 mile hike depending on the site) and you won't have the amenities you'd find in a traditional campground, if you're looking for that. I've only stayed at the park-and-pack sites - but that's my preference.
Not that I'm aware but it's not expensive
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