The most correct opinion is that touching a woman does not invalidate Wudu at all whether it is with desire or without desire.

Rinsing the mouth and nose in Wudu is proven from the actions and words of the Prophet and they are included in washing the face. So if a person omits rinsing the mouth and nose when purifying himself, his purification is not valid, whether he did that deliberately or by mistake.

This is how to wipe the ears in Wudu: The insides of the ears should be wiped with the forefingers, and the outsides with the thumbs. It is not required to follow the cartilage of the ears when wiping.

If there is any barrier such as grease, paint, wax or glue that prevents water reaching the skin, then Wudu is not valid and prayers offered in that case are not valid.

There is nothing in the Hadith to indicate that it is recommended to do Wudu for every Sunnah prayer. The Hadith of Bilal indicates that it is recommended to persist in doing Wudu, and that it is recommended to offer a prayer immediately after doing Wudu.

The mere feeling that something has come out of the back passage does not break your Wudu. You do not have to repeat the prayers that you have offered because you were in a state of Wudu and you were not sure that there was anything that would invalidate it.

Allah exempted the sick from having to do Wudu with water and has allowed them to do Tayammum. If Wudu will harm your skin or delay your recovery, then you should do Tayammum, and there is no sin on you.