I've been to parties here before. I don't think you have to ask permission. There are small sitting areas outside near the swings. It seems to be a first come type deal. As long as you keep it respectful there should be no problem. I'm not completely sure about this but that's what it looks like to me. Also they have space inside from what I understand but I'm sure you would have to contact someone about those.
I have seen Birthday parties there, but not sure if you have to contact anyone to let them know you are having one.
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