Hmm, tricky. It's not 100% clear from this extract whether 'it' refers to his fear of travel or the act of talking about it. I can help you with the meaning of the last sentence though. In the famous book, 'The Picture of Dorian Gray', by Oscar Wilde, the main character, Dorian is very handsome for much of his life but towards the end of the book, he turns very ugly, and all the 'sins' and bad stuff he's done shows on his face (I won't tell you why so as not to spoil it for you, in case you decide to read the book). So in the two sentences, "My face must have been the Picture of Dorian Gray. At the end, when he goes to pieces." he is saying that his face must have looked ugly and unpleasant, just like Dorian Gray's did at the end of the book. To go to pieces means to fall apart or to become bad/worse. Hope that helps.

Yes, "it" refers to his fear. Dorian Gray was a character in the novel "The Picture of Dorian Gray" in which Gray has a painting of himself which ages and shows the ill effects of his hedonistic and criminal lifestyle, while he remains youthful. At the end, feeling guilt and remorse, Gray stabs the painting and dies and the painting reverts to its original beauty while Gray's corpse appears old and decrepit. The narrator is saying his face must look like Dorian Gray's did at the end of the novel.