Is there a picnic area?

Yes Toledo zoo has many picnic area s

Yes

As long as you're outside and in the grass, you can picnic anywhere. The old "Big Cat House" is "The Carnivore Cafe" and offers outdoor seating to anyone.

Yes. It's very big also and has a covering. Also if you wanted to sit in the grass you can in other places

There are many areas with tables where you can eat, some with umbrellas for shade. You're allowed to bring in coolers with your own snacks or there are plenty of places that sell food and drinks.

Several. Located near the amphitheater for sure.

Yes a couple of them. It will show you on the map that you het at the gate.