I'm not sure what you mean by "come to reason," but I can answer the first question. For me there isn't a single most ridiculous statement, but a reoccurring statement that happens over and over again. It's actually most of the first paragraph. The narrator tries several times throughout the piece to assure the reader that he is not crazy. He says it over and over again. It's like he's trying to convince himself that it's true. It's like he trying to will his audience into believing him even though his actions say different.
My favorite three ridiculous statements are three sentences in the middle of the first paragraph.
"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."
The narrator is first claiming super hearing powers. The icing on the cake though is his ability to hear the spiritual realms of heaven and hell. I know the narrator says that he is not crazy, but what would you think if a friend of yours claimed he/she could hear voices from heaven and hell?
The narrator's assurances of sanity continue throughout the story. He claims that he isn't crazy because he silently watched the old man sleep for multiple nights. Yeah . . . that's not messed up at all. Or try this section:
"If still you think me mad, you will think so no longer when I describe the wise precautions I took for the concealment of the body. The night waned, and I worked hastily, but in silence. First of all I dismembered the corpse. I cut off the head and the arms and the legs."