Distance-wise, what is the longest distance in which Amaterasu will ignite its target? Does it have unlimited range? For example, if someone used Amaterasu on the moon from the earth, or on the Hokage Monument looking at it from a mile away, would they catch flame?
I believe the range is as far as the user of Amaterasu can see.
Just like what @Minato Sensei is telling, the Amaterasu is based on the user vision. By focusing their vision upon an object the user is able to ignite the flames, the object ignites at the focus of the user's vision. Thus the distance of Amaterasu really depends on the user's vision, from a certain distance the user can't focus anymore. Bear in mind that this technique puts a great deal of strain on the user, usually causing their eyes to bleed. Thus focusing from moon to earth is not possible.