Is it possible to influence the working behaviour of a simple dc motor with an outside electromagnet?
Motors are generally designed to conduct and contain their magnetic flux in a way that as much flux as possible is used for driving the motor and little is lost. As a consequence, flux supplied externally will not easily penetrate the motor. Therefore, a very strong magnet would be required to have much effect when applied externally to a motor.

It is possible that strong magnetic pulses applied externally could cause cause torque and speed variations. The most effective way to get an external magnetic field to penetrate the motor is to position the entire motor in the path of the external flux. The flux path for the linked electromagnet is between the center rod and the outer ring. To have an effect, you would need something like an iron U shape, with the coil wound around the legs and the entire motor in the opening at the top.