I'm not sure how you have managed to convert music purchased from the iTunes Store easily but are having difficulty converting music from other sources. It leads to the question "how are you converting the iTunes Store purchases and why?" Most music playing software should now be able to play Apple's AAC (.m4a) files. A similar question applies to other music; what format is that music in that cannot be handled as it is and if your player cannot play it, why can't you source the music in MP3 format originally?
That said, if I understand your post correctly you want to convert music sourced from CDs, imported digital files etc. that are in one format, to MP3.* (See the two points I make, below.)
iTunes can do that, usually. Certainly the Apple download version can because I'm converting some now from AAC (.m4a) to MP3. I assume (but I'm not one hundred percent certain) that the version of iTunes from the Google Play store can do it as well. Check the steps below to confirm whether the Play store version is capable.
To convert in iTunes we need to change a setting to MP3, then highlight the songs and tap the File/Convert option. The setting to change will appear to be a little odd, but it is the setting to use.
- To set iTunes to convert to MP3, look in Edit/Preferences/General>When you insert a CD>Import Settings and make sure that is set to Import using MP3 Encoder
- Once that setting is MP3 Encoder, go back to your main library and highlight the song(s) that you wish to convert
- On iTunes' top bar menu, tap File/Convert/Create MP3 Version
- This will create an additional copy of each selected song and those files should be placed in the same folder as the original files. I say should because (for unknown reasons) my test has just created a new folder for the album. If you select a song in iTunes you can find out where the file is located by highlighting it and from iTunes top bar menu, choose Edit/Song Info/File>location
Note that there are some file types that iTunes cannot convert, such as .flac files and other specialist files. In that case, perhaps the NCH Switch Sound software can, but you will have to read the help notes in that software for the exact procedure.
* As I prepare this post, two things have occurred to me:
- neither iTunes nor NCH will convert music sourced from an Apple Music subscription. The music is loaned to you while you have an active Apple Music subscription and it is protected from copying and converting
- if you have Apple Music (the app, which is different to the subscription service), Apple TV or Apple Devices installed as part of your iTunes Library, none of the above will work. You would need to uninstall all three apps.