If a device were created to monitor the nervous signals from the heart, including stable heartbeats, rapid heartbeats, etc., and this device were capable of transmitting the "stable heartbeat" to the heart, would this have any adverse or advantagious effects for medical science?
Measuring the electrical signals (=nerve signals) from the heart is frequently done in medicine, it is called electrocardiography. It looks like this (from the same article):
Influencing the heartbear can also be done and is done by pacemakers. Depending on the patients necessities the can permanently stimulate the heart or do this only, when certain criteria are met which makes an intervention necessary to prevent cardiac arrest. Wrong stimulation can in fact kill people, since they go into cardiac arrest when the stimulation of the heart is not correct. This is why pacemaker patients have to stay away from strong magnetic fields which make their pacemakers fail and leave them without proper stimulation.
This technique of influencing the heart from outside is used by defibrillators, which use an electric shock to influence the heart beat. It is used for treating cardiac dysrhythmias, ventricular fibrillation and pulseless ventricular tachycardia, which all lead to death if left untreated. A special form are automated external defibrillators, which measure the an electrocardiogram and then decide by the form of it, if an electric shock is needed.