Question: Even if Turner planned to stage Kale's murder as a suicide, wouldn't the fact that someone who accused a neighbor of being a serial killer, only to turn up dead only hours later make Turner an immediate suspect? I would think that most serial killers wouldn't be dumb enough to risk having the person who accused them to turn up dead in only a few hours no matter if it was staged as a suicide.
Answer: Being a serial killer, Turner is most likely a transient. When he starts to feel threatened (close to being identified as a suspect) or has committed several murders in one area without getting caught, he will sense the need to move on - relocate with a new identity. At least initially, he can portray himself as a law-abiding "gentleman" to reduce/ eliminate suspicion or buy himself enough time to flee the area and avoid getting caught.
Answer: Turner might be considered a suspect based on Kale's accusation, but there would have to be solid evidence, for which there was none. More likely, it would probably be theorized that Kale's recent erratic behavior and emotional state is what led to his "suicide" and that he had become fixated on Turner and irrationally fantasized and falsely claimed that he was a serial killer.
Question: When Mr. Turner brings home the club girl in the green Volkswagen Beetle, he attacks and chases her around the house which is witnessed by Kale. Soon after, Kale witnesses the redhead calmly leave Mr. Turner's house and walk back to her car and slowly pull away. Later on in the movie, Kale already in Mr. Turner's basement, finds the redhead's ID, keys, and even her scalp (or wig?) intact on the table and says, "The redhead from the club - she never left." Who did Kale see leave Mr. Turner's home calmly?
Answer: Along with the wig seen at the end in Turner's secret basement are a pair of high heels. Turner dressed in both of those along with the redhead's clothing to make it seem like she was safely leaving.
Chosen answer: When Kale goes in Mr. Turner's house to find his mom, he finds a red wig and heels (when he saw the girl leaving Mr. Turner's house, that was Mr. Turner wearing the wig and taking her car to make it seemed like she had left safely).