Dropping calories just means your body eventually burns protein scavenged from your muscles. It is meant as a stop-gap measure and trying to live on it will result in a number of horrible conditions. The elevated heart rate is a disrhythmia caused by your, quite frankly, foolish diet. Also, the BMI is a load of rubbish as it does not take into account a person's build type.
If you want to lose weight, extra exercise is the only way to go - burn off extra weight and raise your metabolism. This will keep it off combined with a good diet. Fasting alone will simply guarantee that it comes back with a vengeance as you are telling your body to burn calories more slowly. Did you know that you can burn up to 400-600 calories per hour of moderate cycling? I generally burn 800/hr and therefore may eat as I please and still stay trim, as well as enjoying the benefits to the cardiovascular system.