I pay the doctor before he conducts the surgery.
Can anyone explain to me whether this statement shows moral hazard or adverse selection?
The problem you are facing has probably both: Moral Hazard and Adverse Selection.
We have hidden action by the doctor (you can't really observe his level of effort during the surgery), therefore we have Moral Hazard.
Additionally, you (probably) can not know beforehand of the doctor is a good or bad doctor, so his type (good or bad) is unknown. So, there is hidden information and therefore possibly Adverse Selection. One example could be that a good doctor would never work for the amount you pay, so the doctor you hire is of the bad type.
Remark: I did not define good/bad doctor here, as it could be many different things; a bad doctor could just be a lazy doctor or a badly trained doctor.