However, with Tywin right there, one has to wonder why Arya doesn't use one of her three deaths on him, a man who is warring with her family and planning such in her presence.
Okay, I actually thought about this one when I first saw the episodes, and the way I saw it is, up until the arrival of Tywin, everyone in the camp was pretty guaranteed to be horribly tortured and killed. When he arrives he brings some civility to Harenhall, therefore killing him would indeed be a great boon to her family, but in the immediate she and her friends would be back under the dominion of the assholes who initially ran the keep. So rather than displaying impetulance, she is actually showing restraint and resonability, targetting those who would do her immediate harm and perhaps saving Tywin for later, if at all. It's a great counterpart to the earlier scenes where she is fanticizing about killing Joffrey, Cersei, and the Hound, yet when the time comes she doesn't even immediately think of any of those three.
Just a different perceptive perhaps. Oh and as far as the last one, I have a great answer: it's HBO, so they ate that shit up (figuratively speaking of course).