[D]o you mark me well I have told you that I am nervous: so I am. (7)
We know that feeling, like the way the old nerves clang after that seventh cup of coffee. The narrator obviously doesn't think nervousness is a component of madness. It also seems separate from his "disease."
They heard! – they suspected! – they knew! – they were making a mockery of my horror! (9)
It's quite possible he was right, though probably not for the reasons he gives. His creepiness probably shows through more than he knows. The fact that there are three of them suggests they were already really suspicious before they got there.
It is impossible to say how first the idea entered my brain; but once conceived, it haunted me day and night. (2)
Obsession forces the narrator's version of reality into a narrow tube. If the narrator was thinking about inventing a cure for cancer or something, this tunnel vision might be a good thing. Here, his version of reality is dangerous to himself and others.
[F]or it was not the old man who vexed me, but his Evil Eye. (3)
The narrator attributes almost godlike power to the eye, as indicated by the capital letters. Perhaps he thinks the old man is inhabited by a horrible spirit.
And it was the mournful influence of the unperceived shadow that caused him to feel – although he neither saw nor heard – to feel the presence of my head within the room. (5)
This is an interesting passage because the narrator speaks for the old man. Throughout the eighth night the narrator imagines the old man's feelings, using his own experience as kind of a template, in a fit of pre-murder empathy.
And have I not told you that what you mistake for madness is but over-acuteness of the sense? (6)
Earlier, he refers to this condition as a "disease" – the implication being that it stems from his body rather than from his mind. Comments like these provoke questions about how the body and mind influence each other, and about the versions of reality of the people they belong to.