Yes, mostly. As the body needs more oxygen delivery, the heart rate increases. Exercise and overall good health make the body more efficient in use of that oxygen and thus less need for pumping fast. Of course slow heart rate can also occur with medications and other conduction system problems. A heart rate is "too slow" when symptoms occur. Consult your doctor.
Maybe. Many athletes who compete at high levels of exertion have slow heart rates at rest. This is a sign of a well conditioned athlete. However, sometimes the body's pacemaker located within the heart is not working correctly resulting in slow heart rate. In this circumstance slow heart rate may have nothing to do with good health.