Archie is right; it's obvious that Lizard is the detective. He asked me about the girl and showed me a photo, leaving a business card so I could contact him if I found anything out. However, I don't know why Slonysh is so fixated on the trash cans, which, in principle, belong in an alley, unless she considers the watch a piece of evidence and forgot to mention this assumption.
Regarding the second note, it's just Thorium playing around with his friends, conducting some kind of multi-step game.
As for the blocked individuals and the single murder, and therefore their guilt, I like the line of reasoning, but I don't see the nurse's involvement.