My rear wiper has been broke since I got the car, and a lot of people here have said that the motor breaking is a common problem with MK1 Puntos. However my rear screen wash spray thing doesn't work either, would this happen if the motor had broken?

Not sure on the Punto, but I think on the Cinq/Sei they're on the same fuse.

the screen wash motor is the same for front and back; probably blocked jets or blocked or disconnected pipe; the current to the rear motor is carried through the bare connectors on the rear door and sill; make sure these are clean/nothing partially covering them