I am unable to delete a playlist from iTunes.

I believe you need to connect your phone to the computer you synced the playlist from and remove the playlist from the music that's being synced in iTunes itself. You can only delete playlists on your device if you created them on your device. If you are certain you created it on your phone and it still isn't deleting, then your iPhone's music library is broken, and you'll need to connect to iTunes on a computer and choose to unsync all music from the phone and then choose to resync the desired music to your phone.