Yes
They have a sign at gate that tell you can bring a certain size cooler inside for babies and meds etc, so I think a backpack is ok. I saw others taking in backpacks through detector.
Yes but will be searched
Yes you can hope They do a search on handbags as you enter in to the park
Yes, I have a child and my wife and I bring a backpack diaper bag with snacks, drinks and my brings her purse
We passed through metal detectors and if you didn't set it off they wouldn't search your bag
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