After a final round the decision is between a small number of people. Use the note to address any hesitation you sensed and to state plainly that you want the role — enthusiasm is a genuine tiebreaker at this stage.
Within 24 hours, while the interviewer still remembers the specifics of your conversation.
Email, almost always. It arrives while the decision is live. A printed letter is a nice supplement for traditional industries, never a replacement.
Send each of them a separate note referencing what they personally asked about. Never send the same text to everyone on a panel.