Faraaidh of wudhu

Q: Is the eye mucus permeable when it is soft? It looks impermeable when it is hard.

Q: I prayed Fajr and was clearing up my room and about 40 minutes later I saw something on the tip of my thumb's nail and some bit inside. So I put it under the tap to test it. The bit inside was gone, but there was still some blackish mark on the tip of my thumb's nail, but not on the skin - I believe. So should I make up that prayer or not? Looks likely to be impermeable, but it's on the tip of the nail anyway. Literally the edge.

Q: Does a full sunnah length beard have to be completely wet during wudu?

Q: Is it necessary to remove any rings and bangles when making wudhu?

Q: Is it necessary for one to repeat the masah of the head in the case where one had his hair cut after making wudhu?

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

Q: If a person forgets to make masah of his head in wudhu, will his wudhu be valid?

Q: Could you explain to me how many faraa'idh are there in wudhu and what are they?

Q: After making wudhu in the morning and performing my Fajr salaah, I noticed that there was still some dirt around my eyes. Will this nullify my wudhu or salaah?

Q: During wudhu, whilst washing the arms, is it also fardh to include washing the hands too, or is washing the the arm from the wrist to the elbow sufficient as hands have already been washed previously at the beginning?