If it was me, I would do the roof with metal roofing. You should be able to flash that, unlike pretty much anything else you apply to it. If that is single wall pipe, there really is no flexible material that I know of to seal it that will take the heat. Maybe some glass rope that has been doped with something.
Metal roof, stucco on all but the face and tile the face=my choice.
Brick or stone really will not work with the angles, and if you tile it all, the corner/edge joints will crack. Not might, they WILL.