I really think that accepting a friends request is not the problem - michievious malarky
clicking on a link from that hacked FB account is, but that is true of any suspicious link.
Dunno if you want to warn junior mate he accepted request today that I never sent.
No problems Carl, IMO accepting friends is not a problem - clicking on links from people is - but then that is an everyday consideration anyway.
Usual security precautions that you employ (or should) while on line should keep you safe. We run the risk of rampant paranoia here. Hackers are a fact of life and sensible actions reduce the risk of infection. Strong passwords that are different on every site is a must (you can get encrypted software that stores them for you).
If your facebook keeps getting battered check
Account settings>Security>active sessions>edit and deactivate all sessions that are not your current one.
Edit: Oh and when you change your passwords choose a random word from an email or something and cut and paste it into the new password field - stops key loggers picking it up. However if you still have not found the trojan you might have to consider wiping your disk and reloading from scratch...........