They are a problem at first, but once you get into the routine it really helps! First When you get up, I assume you have horses, sheep, cows ect..., So you sort them out first but when it comes to your chicken be sure to lay out hen feed on the hay because you have a long day ahead of you! Also dont keep them stuck up in the hen house all day, let them out, pick them up and maybe feed them extra!
-If you make mayonasse Be sure not to let the hens eat it, its really bad for there health!
This is also a part of your first question! Its simple, Follow the first steps and most of your hens will lay special eggs in no time!
At one part of the game a clay shop will open and thats when you need to worry about clay. As you said, go into the mine and smash up a few rocks and at a certian level in the mine you dig up clay!
-Mooing and Baaing
Its normal but in your case maybe they need some more brushing and feeding and getting out more, it very scary aint it!
Hope this helped!