The logic behind this story is driving me crazy. The girl makes perverse innuendos, and the boy defends himself by saying he didn't mean it that way, even though he could have simply said she was the pervert. The bet about taking off clothes had two possible outcomes: either he would almost or completely undress, or the girl would be half-naked. You'd have to really try hard to fall for something so perverse. They could have bet on something else entirely. The same goes for hearing her pee and him offering to go outside, but her preferring not to wait.
Her phobia and the solution she offers make absolutely no sense. She's afraid she'll die in her sleep from an unexpected event because no one will notice. If the boy sleeps with her, they'll both be asleep at the same time. Neither of them would notice a fire. The simplest solution would be for him or someone else to stay in the room with her (while awake) depending on when they get back from school. Assuming they are home by 5 PM at the latest, then he or someone else can look after the girl while she sleeps from 5 PM until 11 PM or midnight. On weekends, they can catch up on their sleep using the same principle, but with more flexibility.