If a Quaker breaks of it's entire nail on one finger will the nail grow back. Does anyone know?

It depends on how far back into the toe it goes when its broken. If it broke off right at the end of the tissue depending on how severe the trauma that caused it to break there's a good chance it will grow back unless the end of the toe itself was damaged. Then its not very likely. Most birds are quite able to continue to function just fine even if they are missing a toe nail. I have several birds that are missing one.