Can I bring my own food inside the park or can they allow us to go out to eat in our car and get back in? I have a child with food allergies

We always bring some snacks and drinks for 3 kids.... just enough between meals. I do not think it is a big issue to do so. Yes you can leave the park, they will stamp your hand and then you can get back in.. no problem

Yes on both counts

You can go back to your car to eat they'll give you a stamp to get back into the park

Yes shouldnt be an issue