It’s 2 days at a time when you pay but you can stay for 14 day, you would just pay 7 times.

I can't find anything about a 2 night maximum. Any on-site signage would take precedent over what is on the website. It does look like the place is open for camping. https://stateparks.utah.gov/parks/utahraptor/park-fees/ It's been four years since I camped there. The amount of trash that I found was disgusting. But otherwise, it was a great spot to camp and adventure from.

Check the website. Sounds like it's closed now. Used to be free, dispersed camping, then the government took over. Looks like it's now private.