Mischeifmaker – honestly I am not a hundred percent sure, the powder varietal is kind of like a course powder, and you rub it in at the scalp and then – if you need it – move downwards on the actual hair. My guess would be that the powder absorbs the oil and because its actual “dry shampoo” when you rub it in it prob activates and freshens up.
Dunno – It comes in 2 forms, 1 is a powder and 1 is a spray. I have the powder form, I think you would have to ask your LOR if it is ok for you to use. I have friends/family members alot more yeshivish/machmir than I who use it but I stopped just because I felt weird using it on Shabbos….