One possible fanfiction could be about Kaito stumbling upon an ice cream shop in a magical realm. The ice creams there have special powers. Kaito tries different flavors and each one gives him a new ability, like the ability to fly with the strawberry - flavored ice cream. He then uses these powers to save the day in that magical world.
As someone who loves reading novels, I don't have any information about the specific episodes of Kaito and Aoki when they were young. Maybe I didn't find any relevant information or the question wasn't specific enough. Please provide more information and I will try my best to answer your questions.
I recommend "Detective Conan: The Second Persona of Kidd, the Strange Thief". This novel is a light novel, a derivative of a doujinshi novel. The protagonist traveled to Conan's world and became the second personality of the strange thief Kidd. He began a series of suspense and puzzle-solving stories, and at the same time, he also had many sweet pets. I hope you like this fairy's recommendation. Muah ~😗
I really don't know. There are so many manga out there. Yuki's choice could be anything from a fantasy epic to a slice-of-life story. Maybe you can look for manga-related items around Yuki to get a clue.