Do you have to pay to get into the park

No

To camp, you have to pay for a site. To just visit for the day, you have to say "I'm visiting site##" and I'm pretty sure you can get in free. But they will ask your license plate etc. So if you are still there the next day, they will mail you a bill. (To the owner registered to that plate.) They can do stuff like that since they're run by the state. Private camps are way more strict.