Yes they have a river you can rent tubes and go down it or bring your own. Yes you can have more then one tent... And yes beer is permitted
Turkey Run State Park dies not have rentals for tubes. Swimming is prohibited in Sugar Creek. There is a pool inside the park. You are allowed 2 tents per site with 6 people maximum per site. One small tent with camper or RV.
Book your campsite on reserve America. It will tell you about the sites. Most aren't large enough for more than one tent so Google satellite view is your friend. We had alcohol at our site and nobody said anything about it.
The only answer i can give is you're not supposed to swim in the river but it was allowed on memorial day.
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