Yes, fur is hair, some back hair is fur, depends how thick, no pictures please
Of course it is. If an animal is shedding, and you see the individual hairs, they are call hairs! They're not called furs. Furs are the whole thing, like what you trade in ACIII.
First sentence from Wikipedia: "Fur is a synonym for hair..." http://en.wikipedia.org/wiki/Fur
Yes but fur is not exclusively hair. According to the wiki page, fur usually involves at least two layers of hair and can also describe the overall "coat" of the animal and the underlying skin that holds the hair when its skinned. So in that sense, hair makes up fur and fur is made up of hair but they're not exactly the same.
The problem is in semantics as we tend to assume different words for things necessarily mean that makes them different as Ryan did on the Bombcast. Just because we only use the word "fur" for animals and "hair" for humans most of the time doesn't necessarily make them different or mutually exclusive. It does in this case, in a way, but in usage calling fur hair is perfectly fine because it's hair but a bit more complicated.