What happened when Jerome scanned the book alphabetically?what was the influence of the book on the three friends and what was their decision after discussing about the book?

I think you are referring to when J was reading about diseases at the museum. In a flashback, J. recollects how he once went to the British Museum to research a treatment for his hay fever, and after reading about diseases, convinced himself that he was suffering. This shows J to be rather neurotic if not a hypochondriac. The book certainly gives the men the impetus to take J's doctor's advice and take a trip in the outdoors.