In terms of seeing the dragon outside of Diagon Alley; that follows the narrative of the dragon in the movie. It breaks out of Gringotts and flies over London, walking across rooftops so would be seen outside of Diagon Alley. In the world of Harry Potter if something went above the skyline in Diagon Alley it would be seen by muggles. Diagon Alley isn't like Hogwarts which can't be seen by Muggles but we seem to have accepted that in IOA.