iPhone 5S will not let me restore to a back up before iOS 8.4

It's not possible to restore to a prior iOS verison.

Just click on My Music and it gives you access to your current iTunes music library.

iTunes purchases can only be streamed from the iTunes app.

Try the help in this support article > iTunes Match on iPhone, iPad, or iPod touch - Apple Support

I went into Settings>Music>Show Apple Music>OFF. From there, I open Music, go to My Music, and I can see my music. I can see my Playlists, but if you tap above your Artists list to the red word Artists and the small down arrow next to it, a menu appears and you can select songs. That will show you songs in alphabetical order. Once you start a song, you can see the icon for shuffle, however I'm not sure if it will shuffle your entire song library, or if it is the album that song comes from. I don't have time to test that while I'm typing to you.

As far as promotion, I used my Music app yesterday for quite some time and never observed any promotion/suggestion to sign up for service. You can try te settings I've described and see what happens.

Okay, I set Shuffle, and the first song ended after I posted, and then the second song that started was from another artist and another album, so I hope that answers your question.

Scott Ebright wrote:

I do that and I am limited to playlists or album.

Tap on the My Music icon at the bottom of the scree. Tap Library. Then, notice that, next to the word "Albums", there is a little down arrow. Tap "Albums". You then get a dropdown list that will allow you to select Songs, Genres, etc.

Once that song, is playing, you should see the shuffle icon at the bottom of the screen.

Edit: Chris got there first. But, yes, Shuffle does seem to shuffle the entire library (that's what took me so long!).