Do the Staff of Herding crafting items drop in all difficulties?
Yes, all items drop on any difficulty. I have gotten the plans twice on NM(I already had them from my first Normal kill) and I farmed most of the drops on NM so I would get better XP while doing it.
The Normal Staff of Herding plan drops in all difficulties, but in order to upgrade it, you need to go to Act IV of each of the difficulties and buy the plan from the Quartermaster.