I don't know the reason. That's just a size that Adobe like.
I can't think of a reason, no.
May I see it? http://www.damiensymonds.net/2013/09/grabbing-700x700px-100-crop.html
No.
Ok, great. Well, it should be a very simply matter of adding a white Solid Color layer, and masking it on.
No gradients needed, nor any noise. Very straightforward.