You can use Tiny Player, which is a simple player for iOS:

http://www.catnapgames.com/tiny-player/

Upvoting in the hope that someone has an answer.

As a linux user, my macbook died and no I basically cannot backup my music that I buy from iTunes.

I don't want to stream, I really enjoy owning my music.

and given that they've caused me to lose music before[0] I'd rather keep this.. so, how do we sync without itunes?

And how can I load the music I bought on CDs years ago onto my phone without iTunes?

[0]: https://blog.dijit.sh/importance-of-self-hosted-backups

VLC allows downloading audio/video files from an UPNP/DLNA source. Only reason why I have not ditched the ipad mini yet.