The default location for catalog folders is C:\ProgramData\Adobe\Elements Organizer\Catalogs.
Yes the catalog can be moved, either manually or by using the File>Manage catalogs dialog. If you move it manually, you can double-click on the catalog.pse[version number]db file and it will open in the Organizer from that location.
However, you may find that putting the folder on a network drive, particularly on a NAS, will lower performance. Adobe does not recommend it.