1) It's more likely her Facebook got hacked. OR there are facebook login problems due to site changes at Facebook.
A few other users have reported this.
2) If someone has access to your Nook they could change something in settings to break certain features. If you didn't know those settings were changed, then you would not know how to fix it.
So, in theory, Nook can be hacked.
3) If your sister was downloading files and sideloading apps from elsewhere then malware might have gotten in.
4) I've heard of people having their roomate etc. snoop into their Nook and such. Could it be something like that?
Most likely is that it's just a Facebook website issue. If you change the options and it works then perhaps it's just a mistake on her part.