"Are you cooking a chicken?"
Translation:Kochst du ein Hähnchen?
"Kocht Ihr ein Hähnchen?" <- shouldn't this be "ihr" for the informal plural "you"? If so, this shouldn't be a valid answer should it?
Right. If a group of people is addressed informally, it is "ihr". ("Kocht Ihr ein Hähnchen?" would be correct, if a king or someone the like were addressed but that is very archaic.)
In a subclause the finite verb is at the end. This is a yes-no-question. There the verb is at the beginning.