Speedometer on 2008 BMW X3 moving when engine is off

It sounds like you have a problem with the signal from the car to the speedometer here. The speedometer needle creeping around to 2km/h when the car is standing still is likely to be a problem with the instrument’s calibration or the sensor that is supposed to measure the car’s speed.

The same goes for the speedo needle rising or falling on its own while you’re driving (I’ll assume it’s the needle `accelerating’ you refer to, not the actual car - at which point you have a death-trap on your hands). My money’s on the sensor which is – due to an incorrect battery voltage, a poor earth or an internal fault – sending the wrong signal to the computer that then controls the speedo needle. The problem could also be the speedometer unit itself which could have a bad actuator that is sending the needle haywire.