My 98' XJ likes to drive me nuts... a couple of the current problems. Do you guys think these would be the sign of a bad computer or a short in the harness(s)

Engine off, key out of the ignition... The cruise control module by the battery will start making a loud noise like an electric motor that is dying. Why is it even getting power...?

Red open door light on dash is lit when the engine is off and the door is closed. Open the door, dome lights turn on and the red light turns off. Close the door again, dome lights turn off and the red light is on. If the engine is running then both lights work correctly.

Fuel pump relay will make a slight buzzing/hum and be warm to the touch when the engine is off and the key is out of the ignition.

Needless to say the XJ kills batteries in hours unless I unplug them.