It can happen, but not "You look yourself in the mirror" which I saw as correct when I just wrote "you look in the mirror" which was considered wrong and is obviously correct, since you see yourself when you look in a mirror.
I wouldn't say so. When you look in a mirror, unless you were looking into it at a right angle, you would not see an image of yourself, but an image of the surroundings corresponding to the opposite angle of view.
"Du ser dig i spejlet" could be understood in two ways. 1. "You (deliberately) look at yourself in the mirror." 2. "You (incidentally) see yourself in the mirror." The latter was not accepted. Reported of course.