My windshield washers and rear wiper don't work

Looking at the schematic, you would only have one power to the washer motor, and if the front washer works, the pump motor is probably good, since it is the same. Your switch inputs are all grounding inputs to the module, as well as rear hatch and window ajar. Does the wiper itself not work, because an ajar fault would cause that. I would check all of your powers, grounds, and inputs to the rear wiper module, and if they are all functioning as supposed, replace the rear module. If the rear wiper functions, but no wash, do you hear the pump run? There may be blockage in the liquid line.

Both should be separate problems.

You would not get any battery voltage from the other 2 wires. They are ground circuit wires, one each for front and rear, grounded by the switches to operate the motor.

Either you have a bad switch or grounding point.

For rear wiper, check the wiper control module, inside lower center of tailgate, behind trim panel.