What is the ruling on my refusal to pay the maintenance fee for a video player to the worker, given that I only asked him to inspect it, and he completed the maintenance without my approval, and the device was not fully repaired?

If you inform the maintenance shop that you do not wish to have the device repaired, then you are not obliged to pay for the maintenance; because they performed an action they were not commanded to do, and their action is considered an تجاوز (transgression). However, if the maintenance included the addition of new parts or components, then you must return them to the shop.