A) Any hash is going to be easily circumvented by anyone who owns Photoshop or any image editor. It's only going to catch those dumb enough not to modify the images, ie. most everyone. Doing the hash server side isn't the big problem though, because if you trust the Facebook App then by default you should trust the Facebook web applications.
B) The big problem is you take care of adversarial reporting at the end, not the beginning. If they get a hit on a reported hash, only then do they tell the photo owner and ask for proof that it's their image.
It's bonkers that Facebook expects people terrified of their photos being circulated to send them those images so a Facebook employee can eye fondle them.
This is just par for the course for Facebook, as a business they are so tone death and oblivious to basic human behavior and feelings that it seems like the entire company is infected with the same alleged autism of it's founder.