The odd one there is Georgiansiver's "Answered question" - surely when people say things like "What are you doing going to the theatre"??, surely that's just an idiomatic way of sayingg "Why are you going to the theatre?" I mean, you might think it's an insulting questionm, but there's nothing stupid about the way it is phrased, it's just how the English language works.

What gets me is "Are you doing anything?" when you clearly are doing something, as a way of interrupting you to ask you to do something else. "Sorry to interrupt what you are doing", that is a much politer way of doing it.