Not on OS X. I'm sure I've seen a tiny js library on github that does browser sniffing and gives you the relevant keyboard shortcut. Can't find it now.
There isn't an API for that, but it's super easy to check the current browser/platform and update the text accordingly.
And you don't really need any library: http://www.w3schools.com/jsref/obj_navigator.asp
No, it's an IE, Firefox, Chrome and Opera-thing. All browsers use F11 for fullscreen and i don't think there's an api for reading which button they use anyway. :P