i dont really understand iTunes & how it works

If you download your music purchases (e.g. via the Purchased tab in the iTunes Store app) it should then show in the Music app for playing, and you should be able to play those downloads when offline (the iTunes Store itself requires you to be online, but downloaded music in the Music app shouldn't).

Do you currently have the music downloaded into Music ? Assuming that the phone's iOS version is up-to-date you can decide what to show in it via the Library button at the top of it e.g. if you select Downloaded Music it should only show what you have downloaded (which should play when offline)

As mentioned by King Penguin, there are 2 different Apps on an iPhone that relate to iTunes. The iTunes Store App where you go to buy media, and the Music App where you listen to what you bought.

You cannot create playlists or really play songs directly in the iTunes Store App, and it requires an internet connection to use.

The Music App on the other hand, can be accessed and play downloaded music without an internet connection.

Here's a link to Apple's own manual and the section about how the Music App works.

iOS11 iPhone User Guide - Music App - Apple Support