Yes, the first one is closer to a badge. I believe badges are supposed to be baldheads with colored markings from the beak to under the eye (cheeks). But most call any baldhead with mismarks in the white a badge. Either way, it is a blue velvet (t-pattern). So I would call it a blue velvet badge.
The second one is pied black. You can call it that or a black splash, or a black white flight.
Third is an ash-red velvet (t-pattern) baldhead.
The fourth I believe is ash-yellow. It might be khaki - hard to tell. If ash-yellow, then it is also a t-pattern (easier to call velvet) and baldheaded.
The last two mated together will give you all ash-red offspring (unless the cock is carrying blue - can't tell from the pic, especially since the flights and tail are white). All cockbirds will be split for dilute. You'll probably have all velvets but bars and checks are possible depending on what each bird is carrying.
