Google Music handles song files differently because of the cloud process. Instead of storing them locally with standard filenames, each song is stored on the server to be streamed to your phone. You won't find a song stored on your phone unless you go to that song in the Music app, and select "make available offline". That will download the song to your phone for offline listening. HOWEVER, for some reason (probably legal/licensing and maintaining their database) when each song is saved locally its given a unique identifier (8768894.mp3 etc) and stored in a cache file several layers deep. You won't find it with a file explorer or any other music player unless you know where to look, and even then its useless because you have no idea which track 9876256.mp3 is. The system is set up to only use Google Music on the phone. If you want to use a 3rd party player you will have to sideload your music directly.
Now, as to your desire to get the music off your phone to your PC, that's actually easy. Your music is stored in Google's cloud. All you need to do is download the Google Music manager program and install it on your PC. On the download tab there is a button to "download purchased music". It does what it says.
If you want an individual track, you can also go to the Google Music site and under "free and purchased, if you go to a song and click on the little triangle next to it, it will open a sub menu that has the option to download that song.