*Question has been edited down to a single question (per eNotes policy).
Three men, who reveal themselves to be police officers, show up at the narrator's residence with plans to search the home. Of course, the narrator is naturally suspicious as to why anybody would suspect that a crime has been committed; in his mind, he has carried off the perfect crime. The officers explain that:
A shriek had been heard by a neighbour during the night; suspicion of foul play had been aroused; information had been lodged at the police office, and they (the officers) had been deputed to search the premises.
The quote reveals that the narrator's supposedly flawless crime was not nearly so well-executed as he believed. The neighbors actually heard the old man's final cry at the time of his attack and summoned the police to investigate. Even though the narrator feels extremely confident about his chances of success in getting away with murder--so much so that he gives the officers an extended tour of the home--his guilt and paranoia begin to chip away at his calm demeanor the longer he and the officers stay at the scene of the crime.