Questions, answered plainly.

Steam updates once a day on the free plan and every six hours on Plus. PlayStation, Xbox, GOG and RetroAchievements update once a day on both, and the PC you play on, with GameDock Helper, every six hours. If you have not been in for a week or more, the automatic store syncs slow down, and GameDock catches your library up as soon as you come back. You can press Sync whenever you want the latest, except that on the free plan Steam and store prices can be synced by hand once a day. A few things can only be read from your signed-in browser, such as what you paid on Steam and PlayStation, a private Steam profile's achievements and everything from Epic Games; they update when you press Sync, or on a timer if you turn on the Companion's background sync, which runs every six hours unless you choose anything from hourly to once a day, and only while Chrome is open.