They could be in a situation where they have to work together on a project for the school. Karuizawa Kei is initially hesitant because she doesn't trust Ayanokoji. However, as they face difficulties during the project, Ayanokoji's calm and intelligent approach starts to win her over. Their relationship then blossoms from there. For example, they might have to deal with a tight deadline and scarce resources, which forces them to rely on each other's strengths. This shared experience can be the foundation for their growing relationship.
In the light novel, Ayanokoji is clearly the more intelligent one. He has a unique ability to analyze situations and people's motives deeply. Ryuen often falls into Ayanokoji's traps because he doesn't fully understand Ayanokoji's true nature. Ayanokoji can anticipate Ryuen's moves and counter them effectively, while Ryuen struggles to keep up with Ayanokoji's complex thinking.
Some Karuizawa light novels might be centered around the summer retreats in Karuizawa. 'Summer in Karuizawa' could be about a group of friends or a young couple spending their summer there, experiencing new things, and growing as individuals while being surrounded by the natural beauty of Karuizawa.
There's also Author B who is famous for her romantic Karuizawa light novels. Her works usually feature the idyllic settings of Karuizawa to enhance the romantic atmosphere between the main characters. For example, in her novel 'Love in Karuizawa', she beautifully describes the cherry blossoms in Karuizawa during springtime, which adds to the charm of the love story.
I don't know for sure. The ending of such a manga can be quite unpredictable and might not have been revealed yet. You could try discussing it with other fans to get their speculations.
The development can also be based on personal growth. Horikita is often very focused on her own goals and can be a bit cold. Ayanokoji could be the one to help her see the importance of relationships. Maybe he shows her how a more empathetic approach can help in achieving their class's success. This would lead to Horikita opening up to him more, and Ayanokoji in turn would start to show more of his true self to her. Over time, a deeper relationship could form as they both grow as individuals within the context of the fanfic.