Wayne,yes rooks are legal quarry when taken for crop or wildlife protection,they are part of the corvid family and can be shot with airguns.
I have never eaten rook and to be honest don't really fancy trying it,their diet can include road kill,carrion and the like ,so doesn't fill me with confidence or curiosity.
I am looking into the Weihrauch HW35 for my next airgun,been around for decades and still in production,walnut stock,carbine length barrel,probably stick with open sights for a change,stick with .22 just shoot so much smoother in a springer.