Brown Chickens and egg frequency
When I bought my two chickens I got one brown and one white. The color of egg represents the chicken you will get from incubator. I have gotten brown chickens from brown eggs and white chickens from white eggs.
I found that if I let the chickens outside, the egg laying was more random then if I closed the door and made sure they had food.
The pet function does increase pet's love for you. This in turn will help you get the large eggs. It took a little while but I finally got my large eggs for the community bundle.