i'm sorry if my english is bad but i don't understand one thing: the mark that every student have it´s a moon au (like) a tattoo?

It's both. It shows wewe are one of Nyx's children if wewe have that on your face. It is in the shape of a moon and colored in when wewe are an adult but its not like in real life when it hurts to get a tattoo it just appears on their face when they are chosen. If wewe go to Google au pictures here wewe can see what they look like.

It basically means nyx has picked wewe special as one of her children and basically really cares about you. She cares about all her children except if wewe have a colored in mark it means your special but not really specailer than the rest just special. Its a moon because they sleep during they siku and our night is there siku and they like worship the moon thats why they have full moon rituals.