The next tenant will be Burgundy
Despite the fact that Bob broke up with her, she still seemed as if she wanted to stay around the apartment. Furthermore, she already knows about the crazy things which happen to those living in there, so it wouldn't take her that long to adjust. Plus, her hair is a slightly unusual color, so it's fully possible that she (like, say, Karl) has some magical blood in her veins. The group shown as Eddie's previous friends are actually... (not sure if spoiler tags work in title pages)
The four people who tried to kill Lord Hate and ended up possessing Bob and his brothers. In the flashback with Kyran and Eddie, you can see the silhouettes of three people. One of them looks a bit like Loratio (is that his name?). Maybe there were more than four people who tried to kill Lord Hate, but the four were the only ones to have died (or had their spirits be unquiet). Having Nefarious in there would spoil the whole thing, so maybe he's off-screen? Eddie is like Fall
Not a whole lot of evidence for this one, but Vladic was very set on Eddie not seeing Fall anymore. That's probably because in Parallel Dementia Fall is an Apocalypse Maiden. But when Vladic presses Eddie on why he wants to see her, he responds with "Because she is like-" and then cuts off. The way he always does when asked about himself, be it how he got those scars or whether he has layers (like Fall does). So I think he was about to say "Because she is like me''. This would also explain why he was important enough to warrant Vladic's protection as a child.