Can a recipient keep the recorded message/audio file?
Only if you send a message with an mp3 attachment. If you send a NextMailSM message with the embedded audio link and without an mp3 attachment the recipient will be able to listen to your recording as long as you do not delete it from your account (or as long as it has not been purged). Once you delete the original NextMailSM message the audio link will lead to a non-existing audio file.