If someone feels like a small piece of flesh in anus and after many months feels some pulsation (beating like heart, something like this) and also has a small pain when bowel and a small tear in anus, then what is it? thanks?

What you described suggests an anal fissure. Keeping your stool soft will help with healing. You may take a fiber laxative like Metamucil and drink enough water daily so that your urine is colorless. For the long term you may try to increase your intake of fiber foods. http://www.mayoclinic.org/healthy-lifestyle/nutrition-and-healthy-eating/in-depth/high-fiber-foods/art-20050948