Nah, it changes all the time. Since everyone uses different themes, it's impossible to name an absolute number. But the maximum picture dimensions forum will accept without resizing is 1280 x 2024.
It just sucks, cause it's hard to customize a profile background when they make the avatar so small that it's virtually impossible cause there isn't enough room to really see anything.
Ah that one's tricky, because the size of your profile changes depending on the style you're using; so there's no set dimensions for width or height. Using a seamless image or one with a solid background is usually the best way to go.
I had a Wolf theme not too long ago, and there's some really good Fox sprites out there, try one of those! :)