I haven't had that exact problem. But, the fault to concentrate on is the door-open sensor. Why?...because the other glitches are related to it either in software (the other functions are inhibited when the software thinks the door is open), or in the hardware:
-- wiring (one or multiple wires are compromised, including the one reporting of the door-closed/door-open state). OR
-- door-open sensor is failing

Where to start: I would inspect the hinge flex-harness (open one end of the rubber boot), are any wires showing bare copper?

If that looks OK, I'd next remove the tailgate inner panel to expose the door closure mechanism. If you can locate the door closure sensor wires, short the signal side to ground (power on), and see if the dash display shows door closed -- if so, the sensor is your problem -- either adjust the sensor mechanically to get it triggering, or replace it.