The 2009 BMW M3 4.0 V8 engine lights yellow at regular intervals, occasionally giving an alarm of engine failure and power limitation, and then the vehicle

This fault must be caused by the throttle. You can try to clean the throttle first and accumulate carbon. Otherwise, the throttle servo motor must be replaced. This car has chain timing and does not need to be replaced. Clean the throttle valve. If the carbon deposit is ineffective, the throttle servo motor is very likely.