Since version 6.6.1, the black screen issue with Facebook login is no longer a problem. You can even create a new account and link it to facebook directly from the modded version. That said, it might still be a good idea to keep the “FB Login Method using ver. 5.2.2” tutorial in the FAQ just as a backup. Facebook login tends to act up now and then, especially after big updates. Though bothersome, maybe it's still wise for a new player to have a binded acc before using the mod apk?
Oh, can you tweak Q2 or even make a new Question about transitioning accounts. Something like a heads-up to bind your game to facebook before using the mod. You’d be surprised how many casual players I know have no idea you can even save your progress that way. They just install and play.