To answer your questions:
1 & 3- This is a movie made for kids, so it isn't supposed to entirely make sense.
2- He could've easily followed her and snuck on when she was about to leave.
4- The whole reason she's trying to go to the moon is for her mother, she is trying to make other people believe in the moon goddess again for her mother's sake.
Also, this movie isn't based off of any story, this is just something the storywriter made up for entertainment purposes.
And you really shouldn't tell people not to watch something, the director and the entire cast & crew worked extremely hard on this movie.