Can I use the PS3 to listen to music in the background when I'm gaming?
(I was told that it works with Spotify, so I created a playlist, only as soon as I hit the PSN button everything stopped)
Listen on the phone on the side or something else
No.
With a CFW it would be possible
What's this?
CFW = Custom Firmware
This means that as soon as you jailbreak your PS3 you have more options with it