The hat adapter is a piece of black rubber, round on top & flat on the bottom. There's an arrow on top indicating the front; the round part fits into the hat, & there are slits on the flat part that are formed to fit the top of Scooby's ears (the ears have little nubs on top).
The witch is also someone in disguise, so, yes, there's a double-face. The hair is white! BTW, Scooby's eyes are different from set to set, something which I just noticed.