First, chickens instinctually go home to roost at night, so if you have had your birds locked in for a while, they'll think of that place as their roost and go back home right around dusk. The first few nights they might not--go find those birds and put them where they belong. They'll get it within a week.
As far as egg-laying, a hen will usually go back to her nest box to lay an egg. If they start laying around the yard, then you might try keeping them locked in until noon or so--until they've all laid their egg for the day--and then let them out to range.
Crows won't eat a chicken. Dogs will. We handle predators by vigilance and a shotgun. We also have our birds behind a fence to keep out dogs. Hawks are different--we do lose birds to hawks on occasion. There's not much you can do about hawks, unless you fully enclose the run. Raccoons and skunks and snakes and weasels we handle by having a very tight coop, and any ventilation hole larger than 1" is covered with hardware cloth (not chicken wire).
