Well, the power mirrors usually work with no key in most vehicles, so that sounds normal to me.
The rear defroster, air, windows and fuel gauge however are different. The fuel gauge on mine usually still hovers near where the tank level is at, so that might even be normal. Do the windows still work if you open the door after turning off and removing the key? Some cars let you close the windows, but once you open the door, they turn off.
The defroster has a timer switch to keep it from running too long, it usually shuts itself off after 10 minutes or so. I wouldn't worry too much about that one.
The air shouldn't work without the key. Does the car have a remote starter added to it? I remember from doing instals that some models had the HVAC blower fan connected to ignition power so that it would run if you remotely started the engine, so the heater or ac would warm or cool the interior. It is possible that those wires could be shorted from a bad tape job by the installer or even the fan blower might be connected to un-switched battery power for whatever reason by a previous owner. Although if this just started happening and wasn't like this before, I suspect shorted wires under the dash...
I would make sure you turn off everything when you shut the car off and park it. If the stuff starts going even when turned off, it's probably haunted or posessed by some evil spirit out to get you and you will need to trade it off or have an exorcism done...
