Donkids need a parent or guardian when they are at the park?

Technically no, if they can get in with a ticket they can run around without an adult, wouldn't really recommend it though if you're at all worried.

Not required unless they are a young minor and raising eyebrows. I know teens as young as 13 that have been set loose with a phone or meetup time and location. Wouldn't recommend for young children. Lol. Depends on the kid I guess. Unless it looks suspicious though, it shouldn't be a problem.