What you mean you can't move songs around? Like change the order the songs come in?
Let's say you decide to build a 90s east coast rap playlist. You download Cuban Linx from the Google library and then you download the War Report from some other source like mega upload. You'll be able to move the war report tracks into any position on the playlist and they'll stay, but if you try to move a track from Cuban Linx to a different position they'll move it back within the next minute. Basically the tracks you download from Google library can't be moved to a different slot unless the entire playlist consists of songs you downloaded from Google.
I have noticed that if you cut the Wi-Fi or mobile data off and then move the tracks they'll stay in place but if your phone cuts off Google's servers won't be able to save the playlist so you'll have to start over. Yes, if your phone dies sometimes Google will delete your playlists. If you're lucky their system will make a copy of the playlist they just deleted and you'll have to add the Google library tracks back to the playlist. Basically when your phone dies for some reason they'll delete all of the tracks you downloaded from Google off of your playlists and if you're lucky when you turn the phone back on they will have those songs saved for you so you can add them back but a lot of times they don't.
The only reason I fukk wit Google music is because they have custom radio stations/playlists by eras and it's easy to discover specific music that way. For instance they have a Soul Glo: 80s Jheri Curl Funk station, then they have a New Jack Swing and an African American movie soundtrack playlist. Other than that I would find a better streaming service.