I don't think so.
I think that the only pets allowed are service animals. But yiu can check their website for details
I believe it may be best to contact the site directly. I haven't seen anyone with a pet before but as the other user said, it doesn't mean they are not allowed. However, know that there are deer and rabbits on the site. Your pet may want to run after them.
I can't say for sure. I would suggest contacting someone at guest services. I will say that I have been a few times and have yet to see anyone there with their family pet, but doesn't mean there is no admittance.
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