Can I transfer my Google Play music onto my iPhone?
Solution 1:
you won't be able to transfer your music directly to iTunes.
You can download this music on your computer per Goolge Music Manager and them sync with your iPhone (https://play.google.com/music/listen?u=0#/manager)
Obviously you can use the Google Music apps on your phone too and have the music to play offline too.
Solution 2:
Google has iOS versions of most of their apps.
For music, download the „Google Play Music“ in the App Store, and log in with your Google account.