I've never seen one there but I also have never seen a sign?! I don't think you should bring a huge tailgate one but if it's small and doesn't leave a mess OR cause danger, I don't see why not. Though there might be a long line of folks wanting to purchase from you!!
As long as you keep it off the artificial turf you're good!
I'm not sure if the grill can be inside the fields but I have seen plenty in the park area. In the far back, passing all 3 fields. But I have also never seen a sign prohibiting them inside the fields.
It's a state park, why not? As soon as you drive in there is office on left,
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