I think she survived. At least, my interpretation of the ending is that she finally finished all of the surgey stuff, so he watches the video to see just how far they've come from when she was about to have it. The white hair might be stress-related, because really. Wouldn't you be stressed if this was your daughter? It might be her first school day after getting healthy, which is why he watched the video, to go "wow, we've really come a long way since she was sick".