Fowls and Dinosaurs

So, here's my theory, if the the chicken's closest living relative is the Velociraptor, and they say that the Velociraptor had feathers, does that they might have had other chicken like features? Such as waddles, the weird flaps on the top of the head, and maybe even had the same colored feathers? And does that make it correct to say that males would be roosters and females hens? 

Also would they be able to survive with out a head? Could they run around and even survive for days with out a head? I personally think so, and I also think that they would have chicken-like features.