Hello Nicolle,
The reason not all the offspring have the beards, is because the “Bearded trait” is a dominant trait, and your birds are not pure (heterozygous) for that trait. If you want to improve that trait, make sure to never breed to the non-bearded birds. To get to the point where you don’t see the non-bearded birds will take time. They will never be pure for the Bearded trait, but you can get to a point where it will be hidden, only to reappear when bred to another heterozygous bird.
The white is a sport (mutation). White sports can occur in all breeds of chickens, and in all animals. It’s why we have white chickens today.
I hope this helps.
Kenny