For the first question, the best response is:
He wants to get away with the murder.
The narrator is trying to convince the reader that he is not mad in order to justify his actions and present himself as rational, hoping to evade suspicion regarding his crime.
For the second question, the best response is:
He hears the old man's heartbeat.
The narrator confesses to killing the old man because he becomes overwhelmed by the sound of the heartbeat, which he perceives as a manifestation of his guilt.