It depends on the day. Sometimes Stewie might be in a bad mood and not be as receptive, but on most days, he likely enjoys the special time with Peter and the stories he tells.
Yes, he probably does. If Peter reads Stewie bedtime stories regularly, it could be an indication that he enjoys this activity. Maybe he likes spending time with Stewie in this way and finds it a special moment to bond with him.
It could be adventure stories. Stewie might be interested in tales of brave heroes going on exciting quests. Peter might choose such stories to spark Stewie's imagination before he goes to sleep.
Peter might also tell Stewie some family - related bedtime stories. He could talk about how he and Lois first met, or some funny family vacations they had in the past. These stories would give Stewie a sense of family history and connection, and help him feel warm and cozy as he drifts off to sleep.
It might be a story from Peter's childhood. For example, he could tell Stewie about the first time he rode a bike and how he crashed into the neighbor's fence. He'd probably make it funny by exaggerating how high he flew off the bike and how the neighbor chased him around the yard.
One interesting Peter Brian Stewie fanfiction could be about their adventures in an alternate universe. For example, they might find themselves in a world where all the rules of their normal world are reversed. Another could be a story where they team up to solve a mystery in Quahog that has stumped the other residents. Maybe it involves a strange disappearance or a series of odd events around town.
The moral could be about friendship. If the story is about Peter and his friends at the bar, it might show how they support each other through tough times, like when one of them lost their job. So the moral would be that friends are there for you no matter what.