This line is an incredible clue that it is fake:
>I do not want to go into details about the disease. I do not want to go into the particularities of my life. And because time is short, there will be no comments, no contact address.
Hard to prove false when literally no information is given.
These two lines are interesting though:
>I am 58 years old and I never will 59. I will die in 2013.
>Yesterday, I had the whole life ahead of me. Thirty or forty years, at least. Today thirty days.
Either he's losing track of his lies, he's bad at math or he has unrealistic expectations about life expectancy. If a 58 year old had "thirty or forty years, at least" ahead of him that means that he was expecting to live to "at least" 98 years old.
EDIT: Here are links to Day 2 and Day 3 translations.