[Proto]

1.

Spoiler:

What the Syndrome does as a side effect is heightening your senses, specially your hearing. People with the syndrome could never actually see her, but their hearing was acute enough to be able to sense her footsteps, and what she said to a minor degree. An hypothetical parasite could somehow cause those sympthoms if it somehow affected the behavior of the frontal cortex, though trying to bring real life science won't do much to explain a fantasy disease

3.

Spoiler:

Her origins are explained in a manga arc called Katautsushi-hen. Rather than spoiling yourself I'd encourage you to wait since it has already been translated and scanlated. It is only waiting to be uploaded... one of these days

2.

Spoiler:

It is basically the product of many things. Basically Hanyuu never actually believed that they would be able to avoid their fate. She was just tryinig to maximize the available time Rika and her had, but she never really tried to do something to solve her situation, other than apologizing for being useless (which makes her change of position in Matsuribayashi hen all the more important). Hanyuu has been around as a spirit for 1000 years, however it was not till 100 years before the story that a human, Rika, was able to see her