I have something to share about Monet.
I found this theory in some forums, but I haven't see it here: Monet is a Yuki Onna (snow woman in japanese folklore). Here the wiki for Yuki Onna.
Some features of this character of japanese literature match some elements of Monet and of Punk Hazard´s arc (quotes from wiki):
First
Yuki-onna appears on snowy nights as a tall, beautiful woman with long black hair and blue lips. Her inhumanly pale or even transparent skin makes her blend into the snowy landscape (as famously described in Lafcadio Hearn's Kwaidan: Stories and Studies of Strange Things). She sometimes wears a white kimono,[3] but other legends describe her as nude, with only her face and hair standing out against the snow.[4] Despite her inhuman beauty, her eyes can strike terror into mortals. She floats across the snow, leaving no footprints (in fact, some tales say she has no feet, a feature of many Japanese ghosts), and she can transform into a cloud of mist or snow if threatened. My emphasis
This one matchs the possibility to follow Law with out being noticed.
Second
In many stories, Yuki-onna appears to travelers trapped in snowstorms, and uses her icy breath to leave them as frost-coated corpses. Other legends say she leads them astray so they simply die of exposure. Other times, she manifests holding a child. When a well-intentioned soul takes the "child" from her, they are frozen in place.[3] Parents searching for lost children are particularly susceptible to this tactic. Other legends make Yuki-onna much more aggressive. In these stories, she often invades homes, blowing in the door with a gust of wind to kill residents in their sleep (some legends require her to be invited inside first). My emphasis
So there are legends with Yuki Onnas and parents searching for their children. Does it sound familiar?
This tale from ancient Japan about a snow woman (source):
'The mountain snow woman from a famous Japanese story'
Translated by Clay
A long time ago in a cold northern country, there lived a lumberjack father and son. One winter day, while they were gatherering wood a snow storm began. They rushed back to their cabin to wait the storm out. But the storm continued and the two fell asleep by the warm fireplace. It was so cold, the son woke up. Outside the wind howled and the snow fell hard. Suddenly the door of the cabin flew away in the wind. Snow blew into the cabin and the warm fire went out.
Just then, a beautiful woman with a pure white kimono and seemingly transparent skin came into the cabin with the snow. She went to the father and breathed frosty air on him. He became white as snow and appeared as ice and breathed no more.
The son said, "It's the yuki onna!" He remembered the story of a fearsome woman who comes with the snow to take away the life of people in the night. Having just seen his father killed, the son's body started to shake. Although he wanted to run, his body couldn't move. The yuki onna moved ever closer to the son while blowing white air from her mouth. She stopped just in front of him and said, "You have received my favor. I will let you live tonight since you are so young. However you must never tell anyone of what happened tonight." And she disappeared into the night and snow. He fainted. The next morning, the boy awoke to find his father's body and wondered if he really did see the yuki onna. He never spoke to anyone about the matter though.
A year passed and the snow again began to fall. One night the young man heard a tapping on the door and he opened to see what it was. It was a woman. She said, "I'm caught in the snow. Is there anyway I could stay here tonight?" The young man was nice enough to let her stay and eat with him. She said her name was Oyuki. They talked and talked. As time passed by they grew to like each other and were married. A few years later they had a child.
In the north country another harsh winter came. One of those winter nights the young man looked at the side of Oyuki's face while she was sewing and said, "You know, you remind me of a woman I saw a long time ago. You look just like her." She immediately stopped her sewing and asked, "Where did you see this woman?" He answered, "Just before my 20th birthday there was a snow storm and she came to this cabin. It was the yuki onna!" Oyuki sadly said, "The yuki onna must have told you sternly not to speak of this. Why do you say this?" He replied, "How do you know this, Oyuki?" She slowly stood up and her kimono and face became freezing white. "It was you… It was you..." "That is right. Why did you say that? Now I cannot live with you." He said, "Forgive me, Oyuki!" But she only said, "I will never forget you. Somehow take care of our child. Fare well!" Just then the door flew open and Oyuki disappeared in the snow. The young man searched for her, but couldn't find a trace. (My emphasis)
The two emphazised lines relates another two elements of PH's arc:
"He became white as snow and appeared as ice and breathed no more." –> Could be Monet the person who frozen all those corpses in that creapy room?
"You have received my favor. I will let you live tonight since you are so young.", and the rest of the story about a marriage between a ghost and a human –> Yuki Onna seems to be a ghost that falls in love easily. Any association with Monet flirting with Law?
…
Also, there are Yuki Onnas in some mangas: Bleach, Ranma ½ and Nurarihyon no Mago, Dororon Enma-Kun and others.
Of course, snow DF is different than ice DF (Aokiji). If Monet is a Yuki Onna she would be able to manage snow, for instance hardening it like in Kamakura technique, or turning herself into a soft snowfall. And wings and talons should be Law’s work.
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