Well I don't know about you, but I don't personally have spontaneous arm thrust towards the screen.There's a tiddly chance of a flas positive if the player untowardly puts their hand into the button zone, but there's likewise a chance of accidentally activation trigger buttons on a dual-stick controller if you knock it against your lap/leg. I don't see a low-risk problem as a sound basis for this interface choice.
Nope. 2D position is absolute based on the camera, and depth is 'absolute' and doesn't drift over time.
Then again, the camera isn't stationary, is it, but keeps roaming around to keep the skeleton in view, which makes the positioning relative. Still, if they know where your hand is to power up a button as they do, then depth isn't a problem. Keep exactly their current code except instead of charging a timer by 2D presence, activate it on a minimum depth. If it's not as easy as that, there's something wrong with Kinect's libraries!
Yeah, it should be possible to do a 'quick' button press motion to trigger an action. It'd be suitable for party games.
Or think of a controller + Kinect combo action.