There is a old story to the history of the Karate belt orders: when Japan was in poverty they couldn't afford getting a new belt every belt test so they would start out with white, dye the white yellow, dye the yellow orange, and so on until the belt was completely black of dying.
It depends on the style of karate. In some styles there is a red belt before reaching Black Belt. In others the red belt represents as the 9th and 10th dan (black belt) in karate.
Every school that I know of starts with a white belt.
The yellow comes first then the white comes after. :)
That will depend on the school. Some go from white to yellow. My school goes from white to orange.