If a medication or a medical condition is the cause of constipation, eliminating the offending medication or treating the underlying medical condition may relieve the constipation. However, certain conditions require the use of a medication despite its side effects.
Your heartbeat can be either tachycardic or bradycardic during a heart attack, so no i don't believe you had have a normal pulse rate at the time of a heart attack, normal being around 60-70 beats per minute for an adult. Heart rate does decrease though with age but that doesn't necessarily indicate anything is amiss.
When you are excercising your heart rate will increase because you are using more energy and therefore need more oxygen/nutrients for cellular respiration. The heart needs to pump the blood faster for this to occur.