Re: "Playing Apple Music" "I’m from South Africa".
Sometimes countries or regions introduce governmental import restrictions on items, or other changes made by the providers of the songs may have occurred. You can see current Apple media availability in various South African regions in the article below:
Apple Music seems to be available ok in most African regions, including South Africa.
Availability of Apple Media Services - Apple Support
Eg: says:
"The availability and features of certain apps, movies, and more can vary. If you think an app or other media should be available in your country or region, contact the developer or publisher directly."
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Re: :" suddenly all the songs in my library are shaded and when I try to play it says “this item is not currently available in your country and region”, including to local songs, I’m from South Africa. Please help."
Sorry you are experiencing this issue. Seems Apple Music is not a back-up service however:
Any digital media you buy from Apple can be permanently downloaded on to an iPhone, iPad, Mac, or Windows PC. See: About purchasing movies, TV shows, music, books, and ringtones from Apple - Apple Support
Eg: says:
"Any digital media you buy from Apple can be permanently downloaded on to an iPhone, iPad, Mac, or Windows PC.
Content you purchase from Apple will generally remain available for you to redownload or otherwise access from Apple. Though it is unlikely, content might be removed from Apple Media Services and become unavailable for further download or access (for instance, because Apple loses its right from the content provider to make it available). To ensure your ability to continue enjoying your movies, TV shows, music, books, and ringtones, download all purchased content to a compatible device in your possession.
You can permanently download purchased content to your iPhone, iPad, Mac, or Windows PC. Once downloaded, you can access content without an internet connection, and Apple can’t remove it from your device."
There's more info. in that article above.