Drinking olive oil on empty stomach in the morning is it helpful for constipation and acidity related problems?

No. It does absolutely nothing except increase your fat. Drink more water and balance your diet. That will fix your constipation. If heartburn or stomach discomfort is your problem, see a doctor to rule out medical causes. Also lose weight, stop smoking, and reduce alcohol intake if any of these apply to you.
Fat Calories Myths. Nope. Not in any way. This is a false myth with absolutely no health benefits. Constipation is best treated with fiber and water. Fat increases the chance of constipation.