What is the ruling on describing someone with "this moon that illuminates your night," and is there sin for whoever laughs at this statement?

The basic principle is that it is permissible to praise people and commend them for the good qualities they possess, based on the Almighty's saying: "And speak to people good words." There is no difference in this regard between a man and a woman, provided that temptation (fitna) is safeguarded against. Her comparison of him to the moon is a permissible metaphor, so there is nothing wrong with it.