Hi Peter,
Short answers:
1 - OneDrive works independently from Elements to sync two or more computers to the files in its Cloud. You store your files in the dedicated OneDrive system folder and OneDrive manages syncing from computer to Cloud and vice-versa. Your files and folder structure is always in sync and the Cloud location is also a good backup for those files.
2 - There is NO way to sync your catalogs. You still have to create Organizer backups for your catalogs. Syncing your catalog folders by creating them in the dedicated OneDrive system folder only works for the source computer,
3 - The safest and easiest way for your purpose is to store both your photo files folders and your catalog on an external drive you plug in alternatively to different computers with the same PSE version. Everything is always available and up to date without syncing. You still need an organizer backup to protect both your images and your catalogs.
4 - Remember the process to migrate images and catalog to a new computer or drive:
https://helpx.adobe.com/photoshop-elements/kb/backup-restore-move-catalog-photoshop.html
This is how you can move your files/catalogs to the shared external drive.
Another advantage of sharing on an external drive is that you no longer need the above backup and restore process if you migrate to a new computer.
If you want more safety with the shared drive when your backup disk is not available, you can create your backup folder on the computer itself, and even in the dedicated OneDrive system folder. I mean the backup folder, not the catalog folder.
I do use shared external drives as explained above, and also OneDrive to share extracts of my photo library between different computers and devices.
Your question has been asked several times in this forum but it's not easy to find those conversations. Don''t hesitate to ask for more details.