A.B.
For the cake... one way you could do it is to arrange a bunch of cupcakes in the shape of the chicken, and then frost over all of them as if it was a solid cake. Then when it comes time to serve the cake, the cupcakes can just be pulled apart. this does take a LOT of frosting, though... Buttercream would work best.
As far as activities, don't forget the chicken dance! You could do a scavenger hunt with all of the clues hidden inside plastic easter eggs. Say that the rubber chicken has stolen the birthday cake, presents, or something, but has laid a trail of eggs with clues inside for the kids to follow. You could also do "Duck, duck, CHICKEN!" instead of Duck, Duck GOOSE, but when the chicken is chosen, it has to run around the circle flapping arms and screaming, "BOCK, BOCK, BOCK..."