Go to Safari / Preferences then select the Privacy tab.
Click Details.
Delete all the web addresses for all the sites you have problems with.
Then go to the Safari menu bar, click Safari / Empty Cache.
Restart your Mac. Try one of the sites.
If that didn't help, the keychains for those sites may be corrupted.
Quit Safari. Open Keychain Access /Applications/Utilites
Select Passwords on the left.
Delete the Safari Forms Autofill keychain as well as all keychains for the sites you mentioned.
From the menu bar click Keychain Access / Keychain First Aid. Click Verify. If necessary, click Repair.
Relaunch Safari. Login to Facebook with your user name and password. You should be prompted to save that data to a new keychain. Click Yes when prompted. See if that helped.