5)  What is the evidence that Neptune has an internal heat source?

Starting with the assumption that Neptune's heat comes from the Sun, we can calculate what its surface temperature should be from its distance from the Sun and its albedo. The actual temperature we measure, however, is considerably higher than the prediction, so we conclude that Neptune must be warmed by an additional heat source. Another answer is that Neptune is at about the same temperature as Uranus, an almost identical planet which is only 2/3 as far from the Sun, so Neptune must have some additional source of heat.