Definitely some weirdness here. Some of it is in the plot itself, but I gotta give it a thorough reread to make sure I didn't mess up anything on my end.

Well, I'm confused. Seems to be a pretty complicated read. Some dialogue balloons not being clear on whose it is in an empty panel kinda exacerbated it.

Hmm... Yeah, still confused. Armchair theories welcome.

Right now, my best guess is that Koishi (through an unusual interpretation of her ability) caused the man Tatsuho to think he saw a doppelganger of himself... which caused him to rent out the "Shadow Sickness" book which was a youma book containing an actual doppelganger.

Don't take my word for it, though. There's also a decent chance that my confusion about the plot caused me to mistranslate some ambiguous bubble and pass it forward... or maybe the plot really just is weird.

What Lev said. Every remaining mystery point can be explained away as Koishi screwing around, which is pretty lame but whatever.

I'm late here, but I imagine the point is that Koishi is showing up as the person that the viewer unconsciously would expect to see in that situation. Akyuu often visits the book store, a relative of the man's at his house, a doppelganger of herself once the mailman informs her of the doppelganger story (and his loner status,) then Keine when Kosuzu needs to be saved. As for why the man saw himself in Koishi, don't think we're even given enough information on him to really know why. Perhaps he rented the book BEFORE seeing Koishi, causing him to imagine her as a doppelganger, or maybe he's just heard of the legend before