Yes you can bring food to eat in the parks.

As for strollers, if your double isn't really strong, sturdy and able to be quickly folded, rent one locally. They deliver to your hotel. And they pick up. I use 'Orland stroller rentals'. (I think) It is worth every penny. You'd be surprised how much you walk, carry and punish these things - we made the mistake of bringing our own double the first trip, never again!

Cheers,