Faraaidh of wudhu

Dirt or sunblock remaining on one's face after making wudhu

Q:

1. After making wudhu, dirt on the cheek remains even after washing the cheek, is the wudhu valid or must the that part of the face be washed again?

2. After making wudhu, sunblock on the face remains even after washing that part of the face, is the wudhu valid?

3. After making wudhu, the dirt (like sand which you normally find when awakening from sleep) remains in the corner of the eye even after washing that part of the face in wudhu, is the wudhu valid?

Nail polish

Q: I know that anything that stops water from entering your skin is haraam (nail polish, wax, etc). But if I only do white nail tips, or any colour nail polish on the tips of my nails which isn't touching the skin. Is this ok!

Finding a black mark on one's finger after Salaah

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.