In the Firefox preferences go to the Privacy tab and select Use Custom Setting for History in the History section. From there you will see the check box to accept 3rd party cookies. Keep in mind this will prevent webmasters from using things like Google Analytics. Which you may want anyway but I thought it was worth mentioning.
Based on the small amount of testing I did on couple versions of Firefox, disallowing third party cookies means only websites you are directly visiting can read or write any cookies.
So if you go to facebook.com and it sets some cookies and later you go to somerandomblog.com that has some images from facebook.com, Firefox will not send cookies to facebook.com, since you are not visiting it directly.
Good question and I'm not sure. I would guess that if it doesn't accept them then it wouldn't read them either. The first step in the cookie transaction would be to check whether that cookie already exists (an attempt to read the cookie). It would seem easiest to stop that process at that point based on user preferences rather that just programming it to check at the actual write time.