You probably need new gaskets in your faucet.
The valve is not be diverting all the water. This valve may need to be replaced.
Yes, remove your old shower valve and fit a new Moen anti-scald valve. This will not change when other items are turned on.
Your suspicion is correct. Sounds like the fan is running continuously. You must have that problem solved to correct the issue. The fan should stop when the ignition is turned off. Sounds like a stuck relay.
30 minutes
It is not supposed to be on when engine is running unless there is a problem.
My probe will not shift to any gear while running but will when turned off. Before taking it to a mechanic I would like a general idea if this is a clutch or transmission problem.
The shower valve needs to be repaired! As for the water not shutting off when you turned off the main that is also needing replacement when it shut of by turning on other faucets you were simply diverting the flow from the leaking main shut off.
You need to check your hot/cold handles or the shower spicket. Not sure what type you have, but they come off. More than likely you need to just replace a gasket..
the shower might be turned the wrong way so they can't use it or something could be blocking the shower the path to the shower.
Try getting the PCV pipe replaced. Mine had a problem with it conking-out at stops and on turns and that turned-out to be the problem. It could also be a vacuum leak.
Perhaps your radiator fan is staying on after the car is turned off. I have recently had this problem, and googled it. And someone else had the same problem.
Its a loss in water pressure to the shower.