(1) From a Buddhist perspective, maybe WE are the p-zombies!
I am a sentient being. I am well aware of this. I cannot speak for others in this regard.
(2) Do we say that our ordinary physical bodies are p-zombies? If not, then why would a nirmanakaya be one?
Our bodies are brought about due to karma. A nirmanakaya is not dependent on karma. It is best described as a reaction rather than as the ripening of willed action (karma).
(3) There is a tradition to the effect that Buddhas lack discursive thought, but act spontaneously. Does "consciousness" imply discursive thought?
Consciousness is a reaction between the sense faculty and object. If a nirmanakaya is an illusory body, then it lacks actual sense faculties, hence no objects are perceived.
Buddhas and bodhisattvas on higher levels are said not to perceive sentient beings. If they did perceive sentient beings, this would not be true wisdom where objects are not perceived.