If the wiper arm can be moved by hand then as you say there is either a nut/s loose or something else is broken or the nylon gear/worm drive inside the wiper motor gearbox is damaged/striped of some teeth.
The running all the time problem could be one of the Yellow relays being faulty or the wiper stalk is causing the fault somehow, perhaps not in the twisting part of the switch but further down where it enters the steering wheel.
A wiper motor, that has no faults, when turned to 0 will switched off automatically and come to a stop when it has finished its cycle, it doesn’t know where the wiper arm is on the screen, the fact that the wiper arm didn’t park correctly is solely down to a loose nut on the mechanism which has knocked the wiper arm out of sync with the motor.
Dec
The running all the time problem could be one of the Yellow relays being faulty or the wiper stalk is causing the fault somehow, perhaps not in the twisting part of the switch but further down where it enters the steering wheel.
A wiper motor, that has no faults, when turned to 0 will switched off automatically and come to a stop when it has finished its cycle, it doesn’t know where the wiper arm is on the screen, the fact that the wiper arm didn’t park correctly is solely down to a loose nut on the mechanism which has knocked the wiper arm out of sync with the motor.
Dec