Can we exit the park to have a picnic lunch and return the same day?

Yes. Keep your ticket with you.

Yes - Just be sure to get a stamp at the gate before leaving the park.

They will ask if you are returning and they will stamp your hand or at least they used to.

Yes you can

Keep your parking receipt if you want to leave altogether so you can reenter. Get a stamp to reenter the park.

Yes

To add on to Lucinda yes they do still stamp your hand and will let you back in.

They still stamp your hand so you can reenter.