The correct answers are We must nip this rumor in the bud before the press arrives. and Since the suspect confessed, his fake alibi is a moot point.

"Nip it in the bud" is a gardening metaphor meaning to stop a problem while it is still small (a bud), before it can grow into a flower.

A "moot point" is an issue that is no longer relevant or debatable. "Mute" means silent, which doesn't make sense in this context!