I scheduled a playlist to begin at a specific time of day, but it did not start on time -- it was several minutes/hours late.
The AutoDJ will never interrupt a track to change playlists. That is, if a playlist is scheduled to start at 10:30, and a 10 minute track starts at 10:25, the scheduled playlist will be deferred until 10:35 to allow the track to finish. This is a common cause for concern for stations which play "mix tracks" which may be an hour or more in length.
The reason for this is because none of the streaming source software currently available on Linux (and thus usable as an autoDJ) supports interrupting tracks during playback -- they only allow an external program (like MediaCP) to choose a new track after each song completes. As such, there is no way for MediaCP to tell the autoDJ to stop in the middle of the track and skip to another song, so this feature cannot be supported.
Several songs played after the scheduled playlist's time -- is it because of the above?
No, the above scenario takes place when ONE song starts just before the scheduled playlist's start time -- the scheduled playlist should start immediately after that song completes.