Wudhu

Q: If I apply coconut oil on my hair, is my wudhu valid after oiling my hair or do I have to wash my hair with shampoo?

Q: During wudhu, is it necessary to put water in the nose piercing (hole), and then twisting the nose stud? Or when one washes the face 3 times is this sufficient. I usually drip water on my piercing and twist the stud but sometimes I forget to do this and get worried in case my wudhu was not valid and if wudhu was not valid then the salah was also invalid.

Q: Does mucus that comes out of the eyes break one's wudhu?

Q: I had an eye operation performed on my left eye. Since the operation, I have not allowed water to touch my entire face. When making wudhu, I washed all the limbs besides my face and when making ghusl, I wash my entire body starting from my neck going downwards. Are all the salaah performed in this state valid or do I need to repeat the salaah?

Q: I came to know about the hadith of Nabi Muhammad (sallallahu alaihi wasallam) that wudhu is not proper if we don't say Allah's name before wudhu. I didn't know about this. So I mostly made wudhu without saying Allah's name. Was my wudhu accepted and am I sinful?

Q: Is wudhu valid with lipstick on lips?

Q: Why is wudhu not valid if someone wears nail polish? Wudhu is a matter of cleanliness, so if anyone wears it after cleaning their nails then the dirt will only touch the nail polish. When performing wudhu, the nail polish will be washed. So why should the water should reach the nail? 

Q: I read that while performing wudhu, we should wash our face upto the hairline. But if someone's hair has receded and his hairline has risen above the normal position or he has lost all his hair and become bald, then where should he wash his face till?

Q: While taking a shower, will the wudhu be done or is it compulsory to do the wudhu separarely?

Q: Is it necessary to wash the area between the sideburns and ears in wudhu?