What should I do about the obsessive thoughts of divorce that I suffer from, and should I act upon the Sheikh's fatwa that I am afflicted by obsessive thoughts and am not accountable for the word "I divorce you" which I uttered by mistake?

It is clear from the question that the whole matter is nothing but waswasah (whispering from Satan), and no divorce results from it. The questioner should, therefore, ignore these waswasah and beware of giving in to them, as their consequences are grave. He should seek Allah's help, not despair, and occupy his time with what benefits him in his religious and worldly affairs.