Faraaidh of wudhu

Q: Is my wudhu and salaah permissible with lash extensions? The extensions are stuck with a glue on the lashes, it does not touch the actual root of the eye.

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: 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: 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?

Q: A person did not wash a part of his body properly in wudhu, or forgot to wash a part completely. He finds this out after he has completed his wudhu and dried himself. Can he just wash that part again to make his wudhu valid or does he have to repeat his wudhu?