Why are her shoes always like that? e_O how does Aya stand up in those?
They're (a Western shoe version of) a traditional Japanese sandals called geta. Geta usually have two bottom pegs (for example, Hoshiguma Yuugi wears those), and single-pegged geta are called tengu-geta. It's a visual pun, because Shameimaru Aya is a crow tengu.
Yes, geta and tengu-geta exist in both historical and modern real-life Japan. I don't get how wearers would keep their balance while wearing them, but then again I wonder the same thing about Western high-heeled shoes, and other people can wear those perfectly well.