Obviously not every event from the show was going to be depicted in play format, but lets say for the sake of argument that a lot of liberties were taken off camera. What other parodies do you see having happened?

For the following episodes:
1. The Warriors of Kyoshi: Basically actor Sokka's sexism would be displayed much like his previous joke: "A woman's place is in the kitchen fixing me meals. I'm starving."

2. The Storm: Can't really think of how to quote most of this, but what I see happening is that Actor Zuko is insulting the general for coming up with such a weak battle strategy, and for whatever reason challenges Actor Ozai to an Agni Kai. But before anything can happen, Actor Zuko accidently hits his own face with the fire prompting the end dialogue:

Actor Lieutenant Jee: I thought he got that scar due to a horrific attack from his father.
Actor Iroh: Nope. Prince Zuko was just a royal klutz.

3. The Deserter: In addition to burning Actress Katara, Actress Aang burns the entire forest down, and thus:

Actress Aang: All in favor of me forgoing Firebending say I.
All three actors: I!!!!