The first part of this question is asking about individual reader opinion. My initial opinion of the narrator could be different from another reader’s opinion of the narrator. It’s more important that you defend your opinion.
My first impression of the narrator is that he is certifiably crazy. He makes an initial claim that some disease actually heightened his senses. That’s odd to begin with, but it's perhaps not out of the realm of possibilities; however, then the narrator claims that his hearing is so good that he can hear voices from heaven and hell.
Above all was the sense of hearing acute. I heard all things in the heaven and in the earth. I heard many things in hell. How, then, am I mad?
He’s hearing voices from heaven and hell. That’s crazy talk in my opinion. The second paragraph continues along those lines. The narrator tells his readers about the old man’s eye. The narrator tells us that the eye really bothered him. So what is the narrator’s solution? Kill the old man to get rid of the eye. That sounds a bit extreme and crazy to me.
I made up my mind to take the life of the old man, and thus rid myself of the eye for ever.
The narrator then tells us about how he sneaked into the old man’s room for seven nights in a row and stared at him. I don’t care how many times the narrator tries to tell his readers that he is perfectly sane. Staring at somebody while they sleep for seven nights in a row waiting for the chance to kill him/her is nuts.
His actions and reasons for those actions show readers that he is definitely insane. Right from the beginning of the story, the narrator tries to convince readers to think that he isn’t a madman.
Ha!—would a madman have been so wise as this?
He repeatedly stresses his sanity throughout the story. He states a total of seven times that he isn’t mad or a madman. He stresses it so much and so often that it feels like he’s not only trying to convince readers; he's trying to convince himself.