Must one remove fat and sweat transferred from the face to the hand during ablution, knowing that it was not present before the ablution?

It is clear that you are afflicted with obsessive-compulsive disorder (waswas). You must turn away from these thoughts and not succumb to them, lest they corrupt your religion. The oils originating from the body do not need to be removed for purification (tahara) to be valid. This ruling is correct because there is no evidence to necessitate it. There is no proof that obligates those with oily skin to do something not required of others. The idea that your dry hand picks up oils and sweat when washing your face, and then you must wash each finger separately, is giving in to obsessive thoughts. The Sharia came to remove hardship and difficulty. Allah Almighty says: "And He has not placed upon you in religion any difficulty" (Quran 22:78). Whoever gives in to obsessive thoughts will be dragged into excessive hardship, and the joy of worship will be taken away from them.