Any fake-Facebook website can copy Facebook's favicon, so that wouldn't add any security at all.
An identicon is a hash value represented as an icon. "facebook.com", for instance, may hash to a red image with a yellow line through it. While you wouldn't remember the icon initially, over time you would – or at least your subconsious would. If you ever visisted a fake-Facebook, you'd immediately notice that something was wrong if the icon suddenly was green with a blue dot in it, for instance.
An identicon is a hash value represented as an icon. "facebook.com", for instance, may hash to a red image with a yellow line through it. While you wouldn't remember the icon initially, over time you would – or at least your subconsious would. If you ever visisted a fake-Facebook, you'd immediately notice that something was wrong if the icon suddenly was green with a blue dot in it, for instance.