For the people unable to login to facebook and get their saves, try to use a different browser. The game automatically opens it in the default phone/tablet browser and some of the older ones seem to give the error. When you get into the login screen, in the top corner there should be an option to open it in a different browser and then you will be able to login normally and get your save going.
No clue about the bans, I only play occasionally, but maybe overuse of skipping the timers and such could tip the developers off?