You can play offline music via the Ps vita or your mobile phone.
Thank goodness. Hopefully you can answer quicker than I can try (yes, being lazy), but can you play music in the background while doing other stuff. Haven't tried to download, but every time I switched to something else (say PS Store) the music stopped.
Yes you can, you need to download your music to your offline playlist. Go to your library section and select the that "..." option beside the playlist, then just tap "Available Offline" and your music will start to download to your offline playlist. Note, you cant have an offline playlist on the ps3 system for some reason...it's only for the vita and mobile apps.