Oh! The blood drinking and her costume gave Kousaka-san away. She's a youkai known as a Hinoenma or Enshoujo, a female vampiric seducer that drains men of their blood and ki to maintain their youth and beauty. They are depicted as young maidens wearing traditional clothes and an umbrella, and reside in remote villages and farm houses. And they have a hidden pair of wings. The difference here is that Kousaka-san prefers young girls rather than guys.

I have a theory about the backstory and possibly the plot of this manga. It's a bit left field, but its cogent.

If you're not familiar with Shakespeare's "The Tempest", there is a major character named Caliban, who is a Cambion (a half man/half demon creature) who was born of a witch named Sycorax. In the prologue, the magician Prospero came to the island Caliban lived on, and defeated the Cambion. Caliban was only loyal to Prospero because of his fear of his master's magic, otherwise his only bit of obedience was extreme filial loyalty to his mother.

Here's the backstory for 1 x 1/2: Ayuko is a witch, a member of a women's only subculture or coven hidden in the modern world. This particular group obtains magical power by contracts to demons known as Incubi (singular: Incubus). An Incubus is a shadowy shapeshifter, a seducer and rapist, known for their ability to dominate humans through magical will. Though considered Male in the West, in reality they are possibly intersex, capable of Male and Female attributes.

Entering into a contract with these demons requires a ritual consisting of the summoning witch, and a sibling pair that plays Male and Female to match the demon's genderfluidity and be both a vessel and a bridge for its spirit form. This is a dangerous ritual given both demon's power and lust. When Ayuko, Atsushi and Akira (hey, alliteration) attempted a summoning, they seemingly lost control of the Incubus, which murdered Atsushi and sexually assaulted Ayuko. And the result was Ayuko being impregnated with Asuka.

I say "seemingly" because Atsushi's death may have been a life-for-a-life blood sacrifice, with Ayuko receiving a half demon daughter that would give her immense magical power required a necessary price paid in blood. But because it killed Atsushi, and because Asuka is dangerously unaware of her power and legacy, Ayuko felt very little warmth for her child. In truth she treats her daughter like a servant or an important work animal, which in fact she is. In spite of Asuka's filial loyalty, Ayuko only begrudgingly accepts her, and was often cold and even borderline cruel in her regard. In fact she has a magical "leash" around Asuka that enables her to suppress her demonic nature, including her sire's lust and will.

But all of that has changed in the course of a few weeks. Which brings us to the incest issue. In small tribal communities, where everyone is a cousin to everyone else, incest is anathema. So much so that they held divine punishment to be quick and decisive. But if punishment didn't happen, then it was because those supernatural forces that governed the world favored the incest. It then would be an opening into even greater magical power. As Akira pointed out, incestuous desire shouldn't occur between a witch mother and Cambion offspring because it is a divinely proscribed taboo (it's too much magic for one mortal to control). For it to be absent is evidence of hidden supernatural agendas. This is why Ayuko indulges her daughter's carnal desires to a limited degree, because she's unsure of the intent or source of this inversion. But some powerful supernatural entity wants Asuka and Ayuko to mate, for unknown reasons, and with an uncertain outcome.

The old woman is the last of her family line. There is no left one to inherit it, and therefore it is useless and forlorn.