Maybe someone can chime in about the milk(I think it just adds fat to the dish), but adding egg to any dish is to keep everything together. It acts as a binder for all the ingredients (think like an omelet or scrambled eggs are like jelloee or some shit). In technical terms it's called an emulsifier.

Posttext - this may all be wrong

Made a pumpkin pie yesterday too, doesn't look as fucking fantastic as yours though!!