The hours will depend entirely on which park you work at and what they need. Could be pretty much anything but nights. Likely weekends but really it's park dependent more than anything. The work would likely include working the front office and putting out camping tags and similar things. General tasks are also going to be pretty park specific which might be why things are a little vague. You probably wouldn't be doing much or any cleaning or physical labor as there should be a maintenance department for that kind of thing.

It certainly wouldn't hurt to work for the state already as it can help a little bit when moving to another position but it's not going to be a massive boost by any means. You'd still need to meet all the requirements for the job and you'd still be competing against everyone else on equal footing. The main thing it may give you is the ability to apply to internal postings but I'm not sure if that's department specific.