Did Wayland actually die?
No, he didn't. The black pills he took were the ones he purchased from Mook (Ellen Burstyn), who also happened to be Phillips' bookie. As he was leaving she said something to the effect of "Careful with those, you take those wrong you go into a coma," to which he replied, "That's the idea." He faked his own death in the interrogation room and Kennesaw didn't want to help him because he wanted him dead since he knew too much about him and his sexual deviance. Remember the EMS crew that picked him up were part of Mook's gang, she knew about the whole "setup," was in on it and helped perpetuate it. The funeral director that talked to Wayland's father was also part of Mook's gang, he was the one who informed Mook that Phillip had been tipped off for the bet that would've gotten him out of debt.
Did Kennesaw kill Elizabeth?
It is possible, it's not what the movie implied but it is possible. If the whole story was a setup and this was a big head game to mess with Kennesaw and his failed life, then that makes a lot of sense as to why Wayland would run this whole setup. Kennesaw's quasi-confession after Wayland's version of the story, helped ruin Kennesaw and whatever life/reputation he had left. If you believe that Kennesaw did kill Elizabeth that doesn't explain why Wayland was in the park at the end of the movie with seemingly bad intentions. You could possibly think that he was merely wanting to replace Elizabeth as his confidant but that wouldn't explain why he looked like he was looking for trouble when he talked to the prostitute at the end.
The movie never clearly states what happened but it implies that Wayland (Tim Roth), killed the prostitute Elizabeth (Rene Zellweger) originally. How did it do that? When Wayland came back at the end, he was the one in the park picking up prostitutes not Kennesaw (Michael Rooker). It can then be deduced that he was the one who killed the original prostitute.