Yeah, it shouldn't need anything more than USB power, it's just another node in the mesh at that point. If you don't have one of those USB outlets just use a phone brick, that should be enough.
EDIT: See THIS for more info. While that's obviously written for Z2M some of it applies to other coordinators.
Not quite I guess, that wafer is what's needed for chip making but from reading the paper it looks like they were just trying to figure out how to make the band gap of the graphene just the right size. It says their next step is trying to adapt silicon chip making techniques to this new material. Terracing I guess to start?