To accelerate a car we ignite petrol in the engine of the car. Since only an external force can accelerate the center of mass, is it proper to say that “the force generated by the engine accelerates the car”?
No, it is not proper to say this. The force generated by the engine rotates the wheels of the car. Now, there is a rolling frictional force on the wheel of the car from the ground. This friction force acts as an external force and accelerates the center of mass of the car system.