Some of these photos appear to be of the European version of the goshawk. The blue/gray bird if ours and a male. See the one where one has captured a"sparrow hawk"? Naturally over here that would be i think a Coopers' hawk judging by the color or a sharp shinned hawk? An American sparrow hawk is our smallest falcon not much bigger than a robin or blue jay and eats primarily insects and some times a mouse here and there...sure it eats birds too .