Can a person that still is paying the bank for car sell to an private individual?

In general, yes as long as the title for the car is in clear, a person can indeed sell their car to another person through a "private sale" agreement even if there's an ongoing car loan for it. When you take out a car loan or lease , your lender or lessor holds your vehicles' clear title until the loan balance or leased is paid off in full. In this sense, you effectively hold a partial interest on the car until it's settled off in it's entirety.