They don't check. You can bring food and stuff.
Small child bag would be fine
Strollers, wheelchairs, coolers with food - no glass. I recommend bringing your own water bottle. They have water bottle filling stations at the water fountains.
No glass, straws or alcohol. You can bring snacks for your kids and drinks. We've brought a mini cooler we kept under the stroller too keep little drinks cold. Keep in mind there is a lot of walking and standing so you want to be minimal so you're not lugging around heavy items.
Coolers, no lids or straws for the safety of the animals, no glass, no alcohol (they do have alcohol for sale in the park), backpacks and they have the right to search anything and everything that you bring. You can get more information on their website.
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