Slicing ice with your fingers (and a bit of graphene)

The 'knife' can't possibly be a single layer of carbon atoms, right? I can see the 'knife', so it clearly must be more than one atom thick (as the video says at 0:55, it's a quarter of an inch thick.)

How is it, then, graphene? Is graphene truly graphene is it's multiple layers thick?

Graphene is one layer thick, but if you stack those multiple layers, don't you get good ol' graphite?

Is graphene really that awesome a conductor of heat? Apparently, yeah.