Well, the lighting in the photos look like lights on the background, and two relatively large lights illuminating their face (you can see the catchlight in the eyes), very possibly some rim light too.
You're spot on about the large aperture, even the ears are out of focus. However, considering how sharp the photos are, its possibly stopped down a bit (but not much at all) and the lens is close to the subject to decrease depth of field. Since he's shooting 8x10 view camera, I imagine the depth of field can be pretty shallow when needed.
As far as camera goes, who knows. But you can get amazing results in a portrait studio setting because of the lighting with many, many cameras these days. Given that he's shooting that many celebs though, I would imagine he could be using something like a medium format hasselblad - but frankly who knows.
Besides all that...check out this strobist post for a behind the scenes look at this photography.
EDIT: That specific video shows the two large boxes like I said, as well as a beauty dish center and up. It looks like he's shooting with a 8x10 view camera.