Does anyone know if there's a way to login ONLY in my Pages iCloud account on a Mac? I'm not logged in in any iCloud services on that Mac, but I would need Pages and my Pages document to sync with my private Mac. (but not the rest!)
You can go to System Preferences and in the iCloud pane there login to iCloud and uncheck everything except iCloud Drive. Then click the options button next to iCloud Drive and uncheck everything except Pages. That should do what you are after.