My guess for (1) is "I am going to be shot." At least then you get a logical impasse...

But you just reminded me of a good one: You die, and instead of going either to heaven or hell you materialize in an antechamber with 2 doors, each guarded by someone who looks just like you. You are told that one is an angel who always tells the truth, and one is a devil who always lies. One guards the door to heaven, one the door to hell, but you don't know which is guarding which. You are allowed one question, which you may ask of one guardian. What do you ask to find the door to heaven?