David,
My best bud/bird dog Apollo (a French Brittany) is an excellent pointer and gun dog. However he knows the difference between chickens and other birds. He loves to point and watch birds at the bird feeder and the birds we hunt, but I can put a chicken on his back!
It's all about discipline and reward. I am the alpha, and the chickens are mine. He wines when I work with them because I am not paying attention to him, and when I let him one to sniff he starts wagging his nub at 4000 RPM, just like he does around the cats!
Bird dogs can easily tell the difference in most birds by smell, otherwise they would point every sparrow and starling instead of phesant, grouse, and quail.
As to the hawks, I have two red sholdered hawks that have a nest just 40 yards from my coop and I don't worry about it. I have a fenced in run, but nevertheless it takes a big bird to carry off a chicken, so they prefer to catch mice and small squirels and other little critters. I've seen them on the ground with the neighbors flock, ignoring the chickens and looking for little critters in the field that they can take up to a tree to eat.
-Jason