What determines the chance to get a brown chicken? Can I get it by incubating white eggs? And what determines the eggs frequency? I noticed that my chickens don't lay eggs everyday, I'm not treating they well?
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.
You can buy a brown egg from traveling cart that appears south of the farm, in Cindersap Forest, on Fridays and Sundays. (The cart usually have a bunch of random items so you it might take a while to find brown egg for sale)
You can also try to keep buying chickens in Animal shop till you get a brown one (just sell white ones back)
From incubating an egg you can only get an animal that lays same types of egg you have put into incubator (e.g. white egg - white chicken)
To increase your chance of getting eggs daily, do not forget to pet your chickens every day, let them outside in all seasons (except winter) and do not forget to feed them.