Is the surgery of fat removal safe?

Depends: It depends on where and what is done. The answer is that It can be safe. There is some risks for this as you need to know of them They would include blood clots, infection and emboli. These would be explained to the patient prior to the surgery. At your age however there should be little need for such surgery and best plan is to follow your doctor's advice.

Relatively: Safe. All surgical procedures do carry risk of complications like infection poor would healing and intra-operative risk. Discuss your risk with your surgeon

Very safe: The advent of tumescent (meaning swollen or engorged) markedly increased the safety of traditional liposuction by diminshing the blood loss and increasing the amount of local anesthetic that could be delivered at one operative session. Although any surgical procedure carries risk, tumescent technique has improved the results when performed by an experienced surgeon.