Transferring one or more songs with all settings and lyrics is already in the works for version 3.6 🙂
There is no playlist folder. Playlists are stored in the database.
To open the song folder, go to settings and scroll down to "Show Stage Traxx 3 Files...".
The files you see are the plain audio files. They do not contain edited lyrics or midi or any other settings. You can transfer them to another device, but you would need to recreate all your settings.
So currently the only way too sync two devices is with a full (or database only if you have no new audio files) backup.
Version 3.6 will then add the transfer of one or more songs. And version 3.7 will feature full iCloud sync.