I think there is some bad spyware on your computer which steals all the data. Also maybe a hacker tried to vnc/remote desktop your computer and succeed.
So there are 5 possible cases:
-connecting to a Wi-fi which stole your fb pass
-spyware
-hacking
-phishing
-remote engeneering
The most popular ones i think are the first one and the second one. I would suggest to remove all your emails from FB , alternate emails , reset passwords everywhere , reinstall your PC....















