I have experienced the first issue - after shutting it down, it starts up again, and if I tell it to shutdown again, it stays off. Even when it's on, if I hold my power button for a few seconds, it turns off, and then turns on again. I have to hold the button again to turn it off for good. (The system is set to hibernate if the power button is pressed, and this works perfectly whenever I press the power button, or if I turn the car off. When I turn the car on, the PC always resumes from hibernation properly.)
I haven't experienced your second issue. When I turn the key to off, the car PC starts to hibernate about 5 seconds after. So that's fine for me. It's never stayed on longer than that.