Thank you very much for correcting my sentences. Here are some more I'm doubtful about.

1) The narrator feels very nervous. A disease has caused (caused??) the acuteness of his senses.
2) He wants to prove to the reader that he is not mad. To prove his sanity he tells the reader his story.
3) He says that he is obsessed with the pale blue eye of the old man which resembles that of a vulture. .
4) For seven nights the old man’s eye is closed and so it is impossible for him to do the work because it is not the old man who vexes him but his Evil Eye.
5) Every night at midnight he goes to the old man’s room. He carefully turns the latch of the door and opens it slowly without making noise. It takes him an hour to place his whole head in the room. When he is just inside, he opens his lantern just enough so that only a thin ray of light falls upon the vulture eye.
6) The following morning he is very polite to the old man and continues to carry out his duty asking the man how he had spent the night.
7) On the eighth night the narrator decided it was now time to commit the deed. (execute the deed).

1. "is causing"

7. Present tenses, please. Use "commit" not "execute."