The hatcheries have a good idea of what the people breeding their chicks are doing, but they don't know or control everything. IDK, it looks blue paint to me. Doesn't look black paint or lavender paint.
Amberlinks are wing sexed, as you say. Whether the hatchery got it wrong is another question. I don't think there is enough to go on to say this chick will be a cockerel, but it bears watching.
The Austra white looks like blue paint to me. Which means her chicks would be half black and half blue when crossed with a black rooster. Half would carry the dominant white gene and be paint, and half would be solid black or blue. Which means 25% of your chicks should be blue paint in that...
It's an impossibly tall order. Small, flighty breeds are generally not broody. Big, docile breeds generally are. As for intelligence, that's more of an individual trait. There's rarely a one size fits all with chickens.
The black, blue, brown and blue, and the white with a little orange are Easter eggers.
The mostly red with a white tail is some type of red sex link.
The thinner, longer white one is probably a Leghorn.
The feather footed one is a light Brahma.
One salmon Faverolles.
The heavier white ones...
The first and last one might be Egyptian Fayoumis. Either that or Easter eggers.
The black and white one you thought might be a Houdan is probably a Lakenvelder.
The buff/white one with the little floof on its head could be a really off buff laced Polish. I can think of nothing else that might...
Keeping them in a secured run is the only real way to protect from birds of prey. Even constant vigilance is not enough with free rangers because goshawks are very stealthy and can strike in the blink of an eye.