As the "Visitor Season" draws more near (and kids are out of school) I'd suggest getting there in the "AM" vs. "PM". We were there for 5 days and each day around 3-4pm, it started filling.

I would say early in the day you should have no problem. And plenty of room for your 24ft trailer.

There are no designated sites so I would imagine you could find something. When we were there a number of people drove a ways from the area nearest the entrance.

I would think so, especially if you're arriving early-ish in the day. We have the same size travel trailer and had no issue finding a spot mid-week. There seems to be a fair amount of turnover for the camping spots. Good luck!