Also when do we ever see a rent notice?

My bad, my mistake. It was a failed delivery notice, I misremembered. Chapter 12 btw.

Still, the people considered it abandoned, but that might happen to any building who is just old. Kou in fact thinks that Nazuna might be into a "dangerous" job when she drags him there for the first time. The building had a working elevator, so that also imply humans uses it. If it was a "ruin" than nobody would be attracted to find Nazuna apartment for her job. Azami did indeed say that, but I felt like he was implying that if a person was believed to be living there then people would be trying to find Nazuna, starting a search. A collapsed empty building would not cause any issue to them. (well, beside Nazuna becoming homeless)

As far as Kos blood tasting good because it has the night in it, I kind of thought that was just an example of Nazuna trying to sound and look cool in front of him.

I don't know how the English translation is, but for the opening line of the anime, the text reads "As for the blood, the night is most tasty".

My personal opinion is that at the beginning the author wanted a more "sophisticated" take on the whole night thing, linking it to the blood. Also, the author wanted a "you are special" element for the MC. As the story progressed and made Kou half vampire, this whole trait was left forgotten. I don't think there is a deeper meaning behind it. But this is a meta-analysis.

BTW I'll add this because I've seen your other replies to other people, but Kou's mother is clearly a hostess. I say this because we know canonically two things: she has an incredibly unsteady income, and she drinks tons of alcohol. Both fits perfectly with the hostess job, and not really with the other kind of "sex industry" jobs. Then again, one of my best friend and witness at my wedding was a hostess (sometimes working even in Japan) for almost six years (she is now a stripper) so I know probably these things better than most.