In conclusion, the mod version 5.2.2 is just a tool for you to log in through Facebook. Because, any version above that can't use facebook to log in or even linked.
If you have linked/binded your game/progress to Facebook—no matter that you uninstall/delete the app and whatnots—you absolutely have nothing to worry about, unless you yourself choose to erase your progress through the in-game Settings.
But, if you haven't linked/binded to Facebook yet, you can only play the game on the same device. If someday the device your game's on is broken—unless you can transfer the game's save file—you can't reload your progress on a new device because you haven't saved your game to fb.