You need a fridge engineer to recharge it as need the correct tools. You may get lucky and this is all you need. If its the compressor I would suggest it would cost you about £150-175 for the repair. The recharge probably £65ish
Yes but likely it is a very small leak that will not be detectable by a leak detector (obviously if it is detectable the engineer will repair the leak). The fact that the compressor is running does not mean it is actually pumping refrigerant around the system.