Hi trjc3rd,
As for your first question, there is no way to delete duplicate items automatically. To delete them, you'll need to follow the steps in the link here: Find duplicate items in Music on Mac - Apple Support
Regarding your second question, the best way to prevent duplicate items is by trying not to add the same songs more than once to your music library.
Lastly, the answer to your final question is a little more convoluted. For example, suppose you subscribe to Apple Music. In that case, you can turn on Sync Library to access your music library and music downloaded from Apple Music on all your devices. This also means that when you delete a song from one device, even duplicate songs, they will be deleted from all of your other devices. Check out the link here to learn more: Turn on Sync Library with Apple Music - Apple Support
Please do not hesitate to reach out to us if you have questions or need additional support.
Thanks for using the Apple Support Communities.
Cheers!