The exposition is the beginning where Elie is describing his family and his people. I would say the exposition establishes the setting by telling us the year and the customs of the people, as well as Elie's attitude and personality.
A major part of Elie's exposition focuses on a minor character, Moche the Beedle. Moche's experience and story is significant because it foreshadows what Elie and many of his people are about to go through. The people's reaction to Moche illustrates that general attitude of the Jews in the wake of the Holocaust. It was not one of fear, paranoia, or hysteria. Quite the opposite, it was rooted in apathy and denial, which is probably surprising to most readers.
As a rhetorical mode, exposition simply means "to inform." Night as a story, is actually not an exposition. It is much closer to a narrative. If your assignment is to write an exposition for the book, you are likely being asked to write an essay. The best way to accomplish this, rather than to simply summarize the story, is to choose one theme of the book, and write about how Wiesel accomplishes delivering the message of that theme. One main focus of the entire book is the sheer death, destruction, sorrow, and survival of those who survived the holocaust. Following one character's journey (Elie), perhaps your exposition could show how he was most effected by the above.
I'm not quite sure what you're asking here. The exposition that Elie Wiesel wrote for Night is quite effective. It shows the reader the fatalistic effects of apathy. The people of Sighet had plenty of warning of the atrocities being perpetrated, but they chose to turn a deaf ear when they were warned. Perhaps it was easier that way.