What are the specific lessons Hannah learns from being transported in time?
I think that one of the most pointed and specific lessons that Hannah learns as a result of her experience is not take her ancestry for granted. At the start of the novel, Hannah shows little regard for being Jewish. Hannah shows little respect for the Judaic traditions in which her family believes and shows a begrudging token regard for what it means to be Jewish. Her experience changes her as she understands about a time in history when being Jewish translated into so much suffering and pain. The traditions and practices that she now takes for granted is something that her experience in time travel will validate, enabling her to have more regard for her ancestry and the people who sacrificed for it. In having more respect for her ancestry, Hannah will be able to learn the lesson of priorities and showing respect for that which is the ultimate definition of identity. At the same time, the novel suggests that Hannah learns that to be Jewish is something that must be lived with pride and zeal because the modern generation is the benefactor of the sacrifices made by the past generations. Hannah benefits because of Chaya and with this, both have a newly validated voice.
Hannah's time travel allowed her to gain a much deeper understanding not only of her heritage but of her actual family members. At the beginning of the story, Hannah seems selfish and disrespectful to the elders in her family and their strong sense of tradition. Her modern life has no room for such "ridiculous" customs. Her eventual understanding of the horrors and self-effacing situations people endured just to stay alive during the Holocaust, brought Hannah to a new level of insight into her families unflappable, enduring beliefs. Faith was the only thing most Jews had left during the Holocaust, and without it, all hope was lost. Hannah now understands how this enduring belief system served a strong, life-preserving role during the Holocaust which has sustained for many to present day.