This is the wrong way around to approach making an external bootable backup. What you need to do is backup/clone the system’s Data volume to an external drive, and then run the MacOS installer on that external drive. The installer will re-configure the volumes on the external drive, keeping your data intact, and result in an external bootable backup. (This is essentially what happens when upgrading from earlier MacOS versions that don’t have separate Data volumes.)
I may have gotten the installation order backwards, but my primary point remains:
If you have a bootable external drive and you constantly perform incremental backups to its Data volume, I think there is a risk that at some point (as your main system’s OS gets upgraded over time) that your backed-up configuration files will no longer be compatible with that drive’s System volume.
Which means you should, from time to time, boot the external volume and run Apple’s software update utility, which is the only way you can update its System volume. Otherwise, you risk breaking the drive’s bootability.
In theory, yes, but I would not recommend storing your library and playlists on an external/shared disk. I just keep the music files themselves on the external disk and use Music/Preferences/Files to specify that location for different users.
The Preference settings and playlists are separate for each user and as long as you give the library folder a suitable name, you can have more than one library for each user. (I have two, with tracks that are used for teaching in a separate library to music.)