The hen who is laying will have an inflamed comb. When they stop laying or aren't laying yet, their combs become a pinkish-pale color.

No they aren't monotremes(egg-laying mammals)

Hopefully your chickens are laying now but usually when you get them they should lay after 2-3 weeks. This is because they need to get used to their new surrounding and the atmosphere.

Snakes, crocodiles and turtles are egg laying reptiles. They are not mammals, as they don't suckle their young from their mother's milk.