In general, watching the anime in release order is the default recommendation, as also for this case:
Nurarihyon no Mago
Nurarihyon no Mago: Sennen Makyou
However, Japanese Wikipedia notes the differences in the anime adaptation from the original manga:
Episode 1 starts with the night-form of Rikuo confronting Gyuki on Mount Nejireme, then it ...
Those are two different Yuki Onna. The one that appears in the first picture is the mother of the one that appears in the second one. If you read the manga, it is explained in further depth there. (Sorry I forgot their names since it was a long time since I read the manga.)
The ability is named moon mirror because as it was explained "nurarihyon is the reflection of the moon" a distortion, and I would say that it means he can first , slow enemy's perception of him to move faster like an after image technique or second, his body ripples like water to allow him to move around attacks. His only weakness like this is cutting the ...