I think the answers to all three are yes, although in my mind, the latter can be very dangerous.

Check out this blog post that Porter Wright published through their Employer Law Report.  They discuss a situation where a company terminated a woman’s long-term disability benefits due to some pictures they observed on her Facebook page.

This is a very interesting debate.  You’ll have to decide if Facebook should have come into play or not.  Personally, I have always preached – if you don’t want someone to see it, never put it online!