Tell Tale Heart

First of all, Poe offers no clear suggestion regarding the relationship between the narrator and the old man. The only inference to be drawn is that they were, most likely, not related by bloodline. In fact, we can only presume that he lived with the old man.
The basic conflict can be seen in the struggle between the narrator’s intellect and his madness. While his intellect retains some control of reason and logic, allowing him to carry out his devious work of murder, his madness, the illness that had so sharpened his senses (especially his hearing) is in full control of his imagination.
Of course, the narrator tries to hide this madness when he begins to discuss his motives for the murder of the old man he had loved. Clearly, this was Poe’s intention.  It lead to the assumption that the character was not insane, yet. Then he confesses he had no desire for the old man's wealth and that  had never wronged or insulted him. There were no passions he felt against the old man and no object of gain or advantage to be had by his death. Later for the first time the realization occurs to him that it was the old man’s hideous eye, his "vulture-like" evil eye. This gives the reader the sense that the crime was an act of compulsion driven by his exaggerated imagination.
In my opinion, I believe the heartbeat was the murderer's hallucination. However the killings were definitely true, although it plants a doubt of how the police quickly appeared. Is it possible to hear the scream from inside the house? In that case the whole scenario can be the character's dream but at this point, the old man was definitely murdered. The negative image portrayed of the old man from the narrator provided a clue of his hidden feelings, leading to crime.