I think caramba is asking if Facebook can see what pages you visit, comment on, SO profile information etc. Such a feat is entirely possible through a cookie when you load any resource from facebook. But when you look at the requests your browser makes, you can clearly see where all the resources are being loaded from. I don't see any requests from Facebook, but I do see many from gravatar.com, the 3rd party service which provides most of the user profile pictures on SE.
But then again, I'm logged in through the StackExchange OpenID mechanism, not a facebook account. You would have to repeat such a test/inspection on an account which is logged in through facebook. As blahdiblah, it's usually the 'Like' buttons that get you on most other pages. I don't see any buttons and the 'share' links by each question and answer are really just permanent link locations, not the increasingly typical Twitter, Facebook, Tumblr, Reddit, Pork'd icon Smörgåsbords.
Regardless, even if SE went to such an extreme, you could block out any such tracking attempt by disabling 3rd party cookies. They're called 3rd party cookies because the 1st party is you, the 2nd party is the website you're talking to and the 3rd party is any outsider snooping agency, advertiser, etc. who tries to listen in.
This isn't a guarantee you can't be tracked. The SE server could, for instance, inform Facebook every time you visit a page and you would have no way of knowing about it. (Or they could log all activity and sell it to the highest bidder.) But as others have already said (or at least,
</tinfoil-hat>), SE does not do such a thing and has no plans to do such a thing.
But there's yet another facet to the debate that we're overlooking at that is you really have no privacy to speak of on an open community site like StackExchange. I, or in fact anyone, can already see pretty much everything you do here. The only solution to that would be to go incognito/private browsing mode, regularly wipe cookies and cache, never create an account or log in or contribute in any way. And even that wouldn't be enough to protect you from the most dedicated and skillful tracker (notably: law enforcement).