Is there a children's play area anywhere in the airport?

Depends where you are. I kniw at Terminal 3, there is a play area near Gate 89.

Yes, in Terminal 3. Not sure about the others. I don't remember seeing one in Terminal 2, so it might depend upon what airline you're flying.

Yes

There is a really nice cushioned one in terminal 1 near gate 23! It looks pretty new. My flight is late at night so with no restaurants open, no television, and a rather quiet airport, the area might suit for a nap! :)

There's one available near Gate 89