Question: What were those things Shang had the recruits wear while having them climb the pole to retrieve the arrow? And how much did they weigh?
Answer: They were weights that he made everyone use to try to get the arrow. It's unknown how heavy they were but they must have been heavy enough to even make a strong guy like Chien-Po fall to the ground.
Question: When Shang finds out Mulan is a woman, Chi-fu (council guy) stops Yao, Ling and Chien from saving her from execution, and says "you know the law." Was there a certain rule back in Ancient China allowing women to get in the army, why was need for Mulan to be executed (almost executed), couldn't they just send her home, why was it a big deal?
Answer: While it was not common for women to serve in the military (depending on the dynasty), they were never put to death. Disney just made this is as a plot device to develop the love interest. The movie is partly based on the ancient poem, "The Ballad of Mulan" and in none of the ancient versions was she ever threatened with execution. In fact, the poem may be based on Fu Hao, a woman who not only served in the Chinese army, but was a military general.
I think that it was an issue, because according to what the emperor said, she basically stole an identity; she "deceived the captain" and "impersonated a soldier."
Question: When Shang mourns for his father's death, Mulan approaches to him and says "I'm sorry" in her normal voice. How come Shang didn't tell she was female because of her voice?
Chosen answer: He just isn't paying that much attention to her voice at that moment. Think about it like this: If you had just lost your father to war, are distraught that you never got to say goodbye, and a male friend you had been training with for some time spoke two words to you in support and they sounded somewhat feminine, would you automatically assume they were actually a woman disguised as a man?
Question: Whatever happened to Mulan's father's sword? The last we see of it is when Shang throws it at the ground in front of her on the mountains. Did she leave it up there?
Answer: When Mulan realizes the Huns are still alive, she can be seen re-sheathing the sword on her horse before mounting it.
Answer: No, he destroyed the statue. The spirit of the guardian survived, but now had no way to manifest itself physically. Presumably, once a new statue was created, the guardian would be able to embody it and come to life.
Answer: No. One theory is that Mulan is the "Great Dragon", as the dragon represents protection, etc, and she protected her family. If you look closely, you can find the Great Stone Dragon watching over Mulan in a few scenes (like in the sword she used to cut her hair).
Answer: For the reasons stated. He believes him to be a highly competent soldier and trainer. While this opinion is probably influenced by Li Shang being his son, it does prove to be correct, as Li Shang's training is what allows the small group to succeed in battling the Huns.