Yes they're allowed. Coolers are also allowed so long as it only contains water bottles not sodas.
Yes, I even saw a tent there last time I went, which was last week. One of those average size. I clearly remember because I had put chairs and set up there but coolers are a whole other story.
Yes
Yes they are allowed and it's good that you bring your own because they don't have any or provide any
Yes there allowed
Yes beach chairs are allowed
It should be allowed
State parks are really lenient .. in short yes 👍🏾
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