Doubts regarding the validity of wudhu when one has an oily face

Q: My face is oily. When I am performing wudhu, some of the oil of my face gets onto my hands. Do I have to rub my hands with water to ensure that water gets underneath the oil and reach my skin?

Do I have to rub any part of my body if the oil of my face gets onto them (for example my forearms, my feet)?

In that same logic, if oil from a part of my face (the left part for example) get onto or mixes with the oil of another part of my face (the right part for example) do I have to rub that area with water (the right part of my face)? 

Giving zakaat to a person that one thought was eligible to accept zakaat

Q: I would like some advice on the following matter:

During this year's Ramadhaan, I distributed a portion of my zakaat to a person who was previously regarded as eligible for receiving zakaat. Today, I found out from a family member that after enquiring from their local Ulama, they found out that this person is no longer a recipient of zakaat.

Please advise whether the zakaat will be accepted or whether I have to distribute the sum of that amount again as Zakaat.

Under eye fillers for dark circles

Q: Is it permissible for me to get under eye fillers for my dark circles? The procedure involves getting hydroponic acid injected into your face to make genetic dark circles look less apparent not necessarily removed but lighter. I look older than I am and it is upsetting as my dark circles are quite apparent. A treatment like this would really help my skin.