Subject 16 has relived Shao Jun's memories
Lucy mentions he lived the life of an ancestor in the Far East, and if you read the blood wall above Desmond's bed, there are multiple Chinese sentences and even an explicit reference to Emperor Jiajing. The young man at the very end of the film was a figment of Ezio's imagination
Think of him as an apparition of Death, in the shape of the personality of Ezio's younger self, telling him his life is coming to an end. What Shao Jun and Flavia were talking about
Shao Jun noticed Flavia hiding from her father and how she peaked her head up and down while giggling, and gave her tips on how to better conceal herself. They're going to practice with hide-and-seek because her father is busy at the moment. The box Ezio gave Shao Jun contains the Masyaf keys
Ezio said that the box was for if she ever lost her way. Altair's memories should help set her back on the right track. And the keys are small enough to fit in the box. And, it would serve the additional purpose of helping to protect the apple in there by sending the keys all the way to China, making it much more difficult for a templar that's aware of the library to find them. Ezio probably left the sixth key in the library, though, no need to tempt anyone with knowledge of the apple.