OK - is number 1 Requiem for a Falling Star? I reckon that makes sense. And I'm sure 2&4 are right but haven't a clue about 3 - will trust all of your superior Columbo knowledge!
Everyone beat me to it. You will just have to trust the fact that I already knew the answers to all four questions -- including the survival of the ploy to make the incorrect guess of "Agenda For Murder" for number 4.