You sure can, many businesses do. For a family or something, it's probably really expensive.
Yes, you're able to. But I'd suggest doing it well in advance to make sure everything goes as smoothly as possible. They're really good about checking in your large groups and running private events, as long as they have the time to prep for everything.
Yes but far in advance
Yes, but only in the evenings. Contact the park for cost and schedule. Schools and businesses do so regularly.
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