Figured it out!! :)
Turned out to be quite simple.. The app didn't show up in the Store (after I wanted to reinstall it) and didn't work for me earlier due to my location settings (both on my phone and in my Nokia Account). Check the article here.
It turns out that for some unknown and stupid reasons (licencing? but why?) the service only works "in" selected countries, and since I had Belgium set as my location both on the phone and in my Nokia account settings the app didn't show up in the Store, and even though I had it preinstalled it wouldn't work (giving me the "We can't get through. Sorry." error when I tried to log in). Once I changed the location setting on the phone to UK the app magically appeared in the store (together with some other great apps, like CNN and SkyNews), so I installed it, and still didn't have the MixRadio etc options, but knowing what the problem was I logged into my Nokia account, change my location there to the UK too, and voila, the next time I opened Nokia Music everything was unlocked, all the mixed radios, saving offline etc, like magic :)
So now my questions are: why the heII would Nokia hide the service from users from some European countries? And why is the Lumia 920 advertised as with free Nokia Music service, if - even though I bought it legally from my carrier - it would not work, without ANY explanation message whatsoever? As I can see now it works perfectly fine in Belgium, the only problem was a stupid setting!! So WHY Nokia WHY??