wood&feathers-
To be safe, poultry need a secure place for the night. It's fairly easy to get chickens to return to the same roost each night, automatically. Just keep them locked in a pen for a week or so, and, when let out, they will return each night. Most of the time..
I've never had a large fowl chicken( yet) hide an egg or a nest off away from their house. The bantams are always laying eggs in some obscure spot, but, I have been fortunate to not have to fight the large/standard size birds in this regard. So, the eggs are NOT hard to find. They are in the nest boxes!!
They are pretty decent layers, I have not had any young hens for a full year, our one young hen got killed by a stupid sheep 2 years ago, and last year ,I only hatched cockerels...This year, is the first year I will have several young pullets/hens to really watch the rate of lay. That being said, my older hens, which are roughly 4-5 years old at least, laid about 50-70 eggs this past cycle, and, they each were broody once, and raising chicks for a good chunk of time. For birds that old, I think that is a fine rate of lay.