The reason why a bicyclist picks up speed on downhill road is because of the effect of gravity and the position of the road. A downhill road is in a slanting position that when a mass or the weight of the cyclist is applied to the bicycle it will cause the bicycle to speed up even without pedaling.
Because of gravity. Just like falling or going down a slide, when you get to the bottom you're going faster than you were at the beginning. Your other question - I think it does violate it because the energy is not staying constant it's actually building.