I intend to use "wall" in the same way that Facebook does.
Does Facebook have any "legal binding" with the word
wall and if so, what?
If you are asking because you are thinking of using the term "Wall" in your own application then you might be on shaky ground.
How shaky that ground would be would depend on many factors - not least of which was how popular your site became. A small site might not bother them, but a high profile site which could be seen as a competitor probably would.
There's nothing to stop you having a part of your application where other users post comments, photographs and links to a page on a user's profile - Facebook can't copyright the idea - however if you were to call it a user's "Wall" then it could be seen as infringing on Facebook to some degree.
Far better to come up with your own term. As to what that term could be - you'll have to give more details about your application, your target market etc.