In her brief marriage, Mizu's husband introduces her to combat with a naginata, which Mizu uses later when her enemies come for her and her husband abandons her. In the Edo Period, a naginata was considered the iconic weapon of a samurai's wife. Her constructing it by adding her weights to her sword might also be an inverse of suriage, the practice of making a sword by shortening a polearm and something that Mizu would be familiar with from her time as a bladesmith's apprentice.
Mikio also explained that a naginata is good for fighting crowds. Sure enough, Mizu used her naginata when she was completely outnumbered.
One of the traits Heiji Shindo says that he hates about Fowler is his smell. East Asians lack a particular gene that gives them little to no body odor compared to Europeans.
Likewise they mention Fowler's fondness for milk as a disgusting trait, in part because lactose intolerance is far more widespread in East Asia.
When Akemi hires Madame Kaji and her girls as her new attendants, she is not just doing it for the warm fuzzies — it's shrewd and pragmatic power politics. Being a new arrival with a still tenuous control over her husband, Akemi has no power base in the palace. By dismissing the ladies-in-waiting assigned to her by the court and instead elevating a bunch of courtesans to this position, she has created a small cadre of extremely loyal agents, whose loyalty to her personally stems not only from their shared life-or-death experience and her magnanimity, but also from the fact that these women are less than nobodies in Edo, elevated beyond their stature by Akemi's will. With everyone else in the palace looking down on them, and as long as Akemi treats them fairly, their well-being and, indeed, survival is entirely dependent on her courtly success. And as a bonus, by managing to recruit Madame Kaji into her faction, as well, Akemi has effectively transplanted an existing command structure to her power base, ensuring that a loyal and very experienced lieutenant will organize her agents if something happens to her.
The end of Mizu's marriage is a parallel to her quest of vengeance against the White Devils: she doesn't know whether her husband or (possible) mother betrayed her, both being plausible suspects, so they both die.
Even if she didn't already recognize Akemi, Mizu would still have known she was up to something when Akemi claimed that Madam Kaji would beat her for failing to service Mizu—that's highly unlikely given what Kaji just told Mizu about Kinuyo. (Kaji does swat her prostitute's hands if they turn down too many requests, because if they want to work in a house that caters to fetishes then they are expect to actually do that, but she's not the kind of cruel taskmaster Akemi is claiming.)
Fridge Logic
The reason why Master Eiji wants everything to always be put back in its place and in exact order is not due to being a hardass, but because he's blind. As such, he relies on the fact that everything in his forge has a fixed position and is possible to locate from memory, simply reaching for the right thing whenever needed.
