I've always thought the Numbers world was a terrible orphanage.
My theory is this: Madotsuki was an orphan for some reason (If you believe she's a foreigner, you can use that here) and had to live in this run down orphanage. The caretakers there (Toriningen) were very cruel to the children and since they had to teach the children as well, they messed around with the children by making them do math, (Perhaps something like "add these large numbers, and if you get it wrong, we punish you"). Meanwhile, the beds there are the sleeping quarters, and the severed head area near the bed could represent Madotsuki being assaulted at that area in the night. I'm going with the Mado was raped theory here, but KyuKyu doesn't necessarily take her virginity.
The caretakers, being the assholes that they are, took it from her, perhaps out of sadism or jealousy. Back in the olden days of English, a maidenhead was a euphemism for virginity. If Japanese is at all like that (And it's always a possibility that Kikiyama isn't Japanese in the first place), then Mado's servered head could be seen as literally a maiden's head. The guillotine obviously is the symbolic taking of the virginity, and the toriningen around the area are the most likely culprits.
Now, the lamppost area nearby could be the surrounding area near the orphanage, which was mostly desolate, and the stream area could be just that. The "A" could be a type of closet or punishment, and the A's are obviously Madotsuki screaming from the punishment.
The area with all of the eye creatures and the strange blue nose thing sticking out in the ground is something I'll need to think about some more. The ways to get into the room could be via Cat effect or knife effect. I think those are the only two ways. My gut wants me to say this also involves something sexual too, but I don't really feel confident (Well at least confident enough given nearly everything in this game is crapshoot) enough to assert that.
The Madotsuki's ghost happens in a closet, in a strange part of the hell maze that is cut off from the rest of the maze. My theory here isn't that the hell maze actually exists (I believe it's purely a dream world area for Mado to travel around a bit easier? Or at least something that connects the worlds together), but that this place is dark area of Mado's mind, perhaps symbolizing some version of herself that feels trapped in the world around her? This might fit well with thePost too long. Click here to view the full text.