As far as the Tale of the Ox and the Donkey, the Vizier is trying to prove a point to his daughter. He is trying to get her to understand that her curiosity will most likely get her killed. That had the Donkey not given the Ox any advice, he would still be laying comfortably, drinking clean water and eating all day. This can be the case for Shahrazad in the eyes of the Vizier. He thinks that she is underestimating the consequences of her willingness to help. That in this situation she will be Donkey, and for trying to help will only end up dead. In the eyes of her father this could all be avoided if she just reasons with him and decides not to go. Shahrazad automatically dismisses the tale, and does not listen to one bit of it. The minute her father finishes the story, she is quickly begging him to let her go and spend the night with the king. She believes her plan will work and that she can get the king to stop killing all the girls he sleeps with. We get the sense that the reason she ignores her fathers words, are because the story does not relate. She does not want to help, out of curiosity, or is doing this impulsively. Therefore she does not believe it will be a miscalculation. She has though through a plan and feels confident that it will work. Also had the Donkey not butted in, the Ox will still be getting mistreated and suffering. So even though it backfired for the Donkey, he helped the Ox out. Maybe Shahrazad does not want to stand by and keep watching all these girls get taken away and killed. She wants to step in and at least try and fix this situation. So in a sense the tale might have even fueled her more to go and spend the night with the king.

So far, stories have been used as proof and reasoning for the decisions characters make.