"TRUE! --nervous --very, very dreadfully nervous I had been and am"
"You should have seen how wisely I proceeded"
"It is merely a cricket which has made a single chirp"
This event shows the present state of the narrator and his personality and without it the story would not have the same eeriness that that the story has with this opening intro.
"His eve would trouble me no more"
This scene is a flashback to the events of the narrator stalking the old man. I think that Poe added this to create tension and a sense of creepiness to the story. Without this part, the story would not have had the same creepiness and would not have established the main motive for the crime that he is coming to commit.
"I smiled, --for what had I to fear? I bade the gentlemen welcome"
This scene is a flashback and I think that Poe added it in too create tension and suspense for what is going to happen next
"I admit the deed"
It takes place in a flashback and the scene depicts the man (Narrator) killing the old man. I think that Poe added the scene to add a weird type of creepiness to the story that it would not be the same without it.
The next scene which is also in a flashback shows the events after he killed the old man with two police officers come to check up on the old man's house after a noise complaint. I think that Poe added in to provide a shock for what is going to happen next. Without this part, the next scene after this would not even be possible due to this scene setting up for the next.
The Next and final scene shows the Narrator breaking down after hearing what seemed to be the sound of a heartbeat. I think that Poe added this in to create a suspenseful and jaw clenching ending and without it the ending would have not been as creepy as this one clearly is.