A grey fox has black on it's muzzle and black all the way down the top its tail to the tip. A coyote will have only a black nose and a black tip on its tail but not the strip down it. A red fox will show a white tip on its tail and no black. The only problem with this is that they are generalizations depending on the area, time of year and animal's age. Also a grey fox's ear will to come to a sharp triangle whereas the coyote's are more rounded like a German Shepard. It is too bad there is no color to go on because that would be a dead give away. As I said, I think you've gotten pictures of 3 dog-like animals: a grey fox, red fox and coyote but, alas, no cougar.
BTW: Note between the 9/04 4:54:09 and the 4:54:10 photos the animal stretches its neck out and looks like that "cougar" in the first set of photos--that pretty much should put the mountain lion theory to rest.