For those in the U.S., all of them either have designated campgrounds or permit primitive camping, even Hot Springs NP.
Yes, you can camp in a state park! I bet you like simple answers because you got one.
Maybe, if you ask permission from your local council, talk it through with them, they might allow it. :)
No. Camping is not allowed at Beltzville. for PA State Park camping,
I don't think pets are allowed within Kakadu Nation Park, but there is a place called Mary River Park located 32 kilometres from the park entrance that is dog friendly. Dogs must remain on a leash....