I like that Kotone is acutely aware of the fact that she has a lot of power over Aoi and doesn't want to, even unintentionally, abuse that power. It feels like a lot of stories with this sort of power disparity ignore that issue or act like the less powerful partner being some degree of on board with it or attracted to their boss eliminates the problem. Though, to be fair, the way a lot of them also include some degree of reversal does help.
What's with homeless people sleeping in literal garbage in manga lol
The Watsonian answer is probably some combination of depression, the trash being softer than concrete, and the trash pile being out of the way. The Doylist answer is that it provides some very clear symbolism for both their mental state and how society sees them.