Thank you all for your helpOn my car the radio stays on until the drivers door is opened, at which point it switches off. I leave the headlights in auto mode, if the are on they go off after about half a minute after the car is locked, however if I lock the car on the fob button and then press the button a second time they go off. The car does the same if you have switched the headlights on manually. I believe it is called the headlight escort facility and it is meant to assist you when leaving the car in dark locations.
Edit: If you leave the lights in auto or manual on they will light up when you unlock the car with the fob, but they switch off when you open the door.