She does the weirdest things for being an experienced assassin.
The code speaking is so on the nose that anyone with a brain listen in would figure they were hiding something. Who speaks about owls and foxes in everyday conversations?
As for the prince, at least this one isn't trusting and dense despite it being off putting to many. The reason he sent her people back was so that she wouldn't have an advantage over them if she chooses to attack when they let their guard down (Ala red wedding style). There is still tension between the two nation, do people really expect him to let his guard down with an enemy in his territory (no matter how sickly she pretends to be)? It would make little sense to do so.