I had to whittle down the original question. I think that the most overwhelming example of naivete in Fitzgerald's work has to lie with Jay Gatsby. Gatsby believes that his dream of winning Daisy is something that can be accomplished through the acquisition of material wealth. Gatsby believes that his dual pursuit of his American Dream and Daisy are going to be accomplished simply by displaying wealth and its trappings. This is an example of naivete because Gatsby does not account for barriers that will prevent his entrance into the world of protected wealth and that he can "have" Daisy. Gatsby believes that she will choose him with the same reckless abandon that he pursues her. This is naive because it fails to account for Daisy's own desire to preserve her sense of self and her situation, forcing her to stay with Tom. In the end, Gatsby's pursuit of his dreams is done through a focus of naivete, a statement that Fitzgerald might be saying of all who are so dependent on their own dreams.
Gatsby was also naïve in the way he went about sustaining his wealthy lifestyle. He was naïve to believe that chasing a married woman would not have adverse affects. For everything Gatsby did, he believed the end justified the means. The end was, for him, love – or at this point it was more like a fascination with his nostalgic memory of her and his fascination with the quest itself; the quest to win her back. To sustain his wealthy lifestyle, Gatsby resorted to business dealings with Meyer Wolfsheim, a notorious gambler, bootlegger and racketeer. In addition, Gatsby attempted to build himself up by appearing to be a prominent socialite, but contradictorily, he built himself up by abandoning the more innocent man he was (Gatz) for a functionally superficial bootlegger (Gatsby). His naivety is largely based on his general assumption that ‘the end justifies the means.’