The only time an Aussie footballer kicks the ball off the ground is when they're under so much pressure,they don't have time to pick the ball up. If you are a defender and you're running towards the ball with the opposition forward, right behind you. You would just kick it off the ground away from him and the goal area you are defending. If you are a forward in the same situation as above, you would have a pot shot at the goals with a kick off the ground. It really does depend on how much time & space you have between you & your opponent. If you pick it up and then get tackled....you can be penalised for being caught in possession of the ball. A free kick is then awarded to your opponent.
Not in Aussie Rules. Rugby League or Union though both require this skill. Actually one aspect of league that I am intrigued you don't see more of in your game is where the player 'rushing' (term is not used in league) pivots in the tackle and 'laterals' to a second player coming through. Is this disallowed or just not considered a reasonable risk to take? It occurs reasonably regularly in league, certainly the players look for the opportunity if it is there. It effectively gains you a second 'rush' on a different vector.