I've been wondering this for awhile but from what I've read on Aki's trope entries, in the manga she's fully aware of the effect she has on boys, but her anime counterpart is utterly clueless. So if she doesn't want that kind of attention, why the hell does she dress in such clothing in the first place?
Revision: finally answered by the flashback in chapter 74. It's because Minori talked her into wearing skimpier swimsuits and revealing clothing back, when they were in highschool. The implication being, that Aki eventually began dressing that way out of habit.
What is Himegeami?
Is she supposed to be a spirit that dwells in a human body? Or is she some sort of physical projection of the spirit that dwells on that mountain?
Neither. Her body is a metaphysical construct of Element that took on Himegami's likeness. In other words: she's a tangible ghost, since she died ages ago while confined within the barrier atop Amanohara.
So let me get this straight: after watching his mother allegedly get beaten to death, by Tesshin, which turned out to be false since she was close to dying anyway, Takeru develops a chivalrous nature where he believes women need protecting. That in itself isn't what bothers me, it's the fact that his mother was one of the freaking owners of a dojo. Wouldn't this basically mean that Takeru has seen his mom fight off challengers/students before and win? If that's the case, why would losing one match equate to him thinking all girls need to be shielded?
It's more a combination that: 1.) she was beaten to death right in front of him. 2.) he took issue with the fact that his dad didn't lift a finger to help her, even though she was losing (badly) and presumably did nothing about it afterward. Which is why Takeru resents his father.
While the first part was eventually proven false, Takeru still developed a fierce predisposition to protect all women, regardless how strong or capable they are of defending themselves. But the manga repeatedly shows that his help usually isn't needed.