They are ready to be moved out now. They are fully feathered. Birds experience temperature drops worse than that when they get older. Your birds need to get out and exposed to the normal weather ASAP so they can acclimate.
If you are concerned about the temperature difference, give them a huddle box inside the coop to sleep in. Basically a box turned on it's side that is large enough to fit all of them in it.
As long as your coop is dry, draft free at the roosts and well ventilated, they will do just fine.
I would keep them on the starter for life. Just offer them oyster shell in a separate container (or two or three) on the side when they hit 16 wees old. Starter has a better protein amount than any layer feed I've found. And keeping them on a starter formula for life enables you to add chicks in the future without having to worry about them eating layer feed when you integrate them. Additionally, when hens molt, they do not need all the extra calcium of layer feed. If you intend to ever have a rooster, they don't need it either. The extra calcium can eventually cause kidney damage in birds that do not need it for shell formation.