The effects of caffeine begin fairly soon after consumption (as soon as 15 minutes) and can last for hours. This, again, varies depending on the plasma concentration of caffeine in the blood.
With regard to the increase in heart rate, as long as someone is not experiencing symptoms such as lightheadedness or dizziness, a temporary, unsustained increase in heart rate should not have any damaging effects. I generally recommend no more than one or two cups of coffee/caffeine daily, as higher amounts can sometimes predispose someone to cardiac arrhythmias, if caffeine is consumed in excess.
And please stay away from those energy drinks! I have seen plenty of young patients in my clinic due to use of energy drinks, which have large and unregulated amounts of caffeine and sugar.