I understand you're trying to edit a playlist and have been unable to, as well as being unable to delete the playlist. You're also experiencing an issue where you're unable to play the songs. I'd be happy to provide you with information to help you out in this situation.
Check out this article. You may need to turn off iCloud Music Library and then reenable it. Keep in mind, this will delete any downloaded music: Turn on iCloud Music Library
On your iPhone, iPad, or iPod touch
- Go to Settings > Music, and tap iCloud Music Library to turn it on.
- If you already have music on your device, you're asked if you want to keep the music that's on your device.
If you choose Keep Music*, the music from your device adds to your iCloud Music Library.
If you choose Delete & Replace, the music on your device is replaced with the content from your iCloud Music Library.
Once you've enabled iCloud Music Library again, try to create the playlists once more: Create and share playlists
If this still wont work, make sure your device is up-to-date!Create a playlist
You can create playlists on your iPhone, iPad, or iPod touch; your Mac or PC; or your Android phone.
On your iPhone, iPad, or iPod touch
- In the Music app, find a song that you want to start your playlist with. Long press or use 3D Touch on the song, then choose "Add to a Playlist" > New Playlist.
- Give your playlist a name, description, and cover image, then add more songs: Tap
Add Music, then search to find a song from your Library or the Apple Music catalog, or browse through songs under Library. When you find a song that you want to add, tap
.
- When you're finished adding songs, tap Done.
By default, songs that you add to playlists don't automatically add to your Library. If you want to add each song to your Library, you can change your settings.
Thank you for using Apple Support Communities.
Have a great day!

Create a playlist