Do they have a rooster or just chickens? If not, the eggs will NOT be fertile (no baby chicks). Even if they have a rooster it doesn't mean that the eggs have been made fertile either. At a certain point eggs can be "candled" to see if a chick is inside.

Running free like that is called "free range". Goid for the chickens because they can eat bugs & natural foods besides their chicken feed. Makes them healthier & their eggs healthier too.

Yes free range chickens lay their eggs whereever they feel it's safe & comfortable for them it they are not put in a coop at night for safety (we have tons of predators around here..raccoon, fox, possum, coyote). When they are free to lay their eggs whereever, finding them is like an easter egg hunt.

Hatching eggs without the chicken is not that easy. It takes a heat lamp & turning them. You would have to research what you would need to buy & do to accomplish that.