[The original question had to be edited to form just one question]
Told from the first-person point of view, the young man who narrates, strongly identifies himself with the old man who lives with him. More specifically, he and the old man, who possesses a dead eye that resembles that of a vulture, become preoccupied with a death-watch in their psychological terror of the consequences of time. In a perverse effort to stop the terror of the narrator's own "I," he kills the old man, whom he professes to love, but states that
...it was not the old man who vexed me but his Evil Eye.....I knew what the old man felt, and I pitied him although I chuckled at heart.
After he kills the old man, the narrator states that the "heart beat on with a muffled sound." Nevertheless, he buries the old man beneath the boards of the room only to discover that he can yet hear the beats of the heart. These beats, of course, are those of the narrator himself. Finally, the narrator can no longer stand the pounding of the heart--his own heart--and he confesses to his crime.