@PenguinSans: I guess part of the equation here is getting a determine on what exact kind of body the FMC has. A zombie, in its most famous iterations, does not actually need to eat food; it may consume something, because of the most basic instinct it possessed in life, but its body does not actually digest it. If anything, her eating food, under these circumstances, would only speed the process of the decay of her body, since she is introducing more and more bacteria-laden objects into her already-dead meatsuit, lol.
Personally, as I've read a number of chapters since this one, I'm more inclined to think that her spirit is giving the
simulation of life to her physical body; that is to say, it functions as if it were alive while it is being inhabited by a compatible ghost. Therefore, it will require sustenance, like any other living human, lest it completely die and become a
true zombie. This is pretty tricky though, since the life of the body also seems to be a tether for Karen, and she likely would not be able to return to it if it totally died. However, this is also tenuous, since it doesn't take long for life functions to halt once the lungs stop working, and the heart stops pumping blood to the brain. We've already seen that she's been out of her body long enough for a human to traditionally die because it stopped breathing, so I don't know how the author would ever explain this. At the very least, she should already have brain damage because of oxygen cell death in her grey matter.
As for your second idea, it's my opinion that ghosts are essentially 'asleep' in this world until something happens to trigger their wakefulness. They are tied to a particular place, but if left undisturbed, they are not even conscious of the world they are in. How many stories have you read about a ghost suddenly appearing because its remains were uncovered in the place where they died prematurely? While they are "asleep", they do not require living essence, I suppose. In the case of the glasses ghost who was eventually untethered by greenhead, she was likely drawing in small amounts of life energy from the workers and denizens inside the office building, just by proximity. The 'chill of death' one might feel while within in her invisible presence is her unconsciously siphoning off a little of that person's energy.
TL;DR, my apologies, lol.