What exactly does the sport setting button accomplish? The car becomes considerably quicker, and in fact, seems to be more stable. So? How?
Also, when my car is warming up, there's a audible 'thumping' noise from the right rear of the car when turning. Seems like it stops after warming up. My imagination? A problem? Or something I should expect?

Sport changes to a more agressive throttle mapping.

For example: When you're not in sport mode, the throttle bodies open up in exact porpotion to the gas pedal. So, if the pedal is at 72% open, so are the throttle bodies.

With sport, the throttle bodies open up more in comparison to the gas pedal. So if the pedal is at 50% open, the throttle bodies will be some open at 60%.

(Figures arn't exact, just examples)

The thumping when you turn may be your diff. Theres a TSB out about this, have your dealer check it.