Hello Wsqwared,
I see you have questions about music you didn't purchase or add being added to your Apple Music library. I can understand wanting to find out where this unknown music is coming from. If you have Shazam installed on your device, and you use it to locate music information, it is possible this is where the music is coming from. Here's information on how to Use Shazam to identify songs and find new music.
This article goes over how songs from Shazam are automatically added to your Apple Music library: Use Shazam with Apple Music, Snapchat, and more
Tap the Apple Music button near a Shazam to listen to that song in Apple Music. If you’re an Apple Music subscriber, songs that you've Shazamed are also automatically added to a playlist called My Shazam Tracks in the Music app. To add a Shazam to a different playlist, tap "Add To" next to a Shazam, then tap the playlist that you want to add the song to. If you’re not already a subscriber, learn how to join Apple Music.

If you can’t add songs to a playlist, make sure to sync your music library with Apple Music. If you don’t want Shazam to automatically add songs to Apple Music, in Shazam on iPhone or iPad tap the library button
tap the settings button
then turn off "Auto-add Shazams to Apple Music."
Do you have any other Apple devices that use your same Apple ID and password? If so, it's possible that you have Sync Library enabled with Apple Music. Here's more information on that: Turn on Sync Library with Apple Music.
Best regards!