The manga and its adaptations may have some differences in terms of character expressions and the pacing of the story. But overall, the core plot remains similar.
The answer to whether Kaori lives in the Kimi no Uso manga depends on how you interpret the story's progression and the author's intentions. It's a matter of in-depth analysis and understanding of the manga's narrative.
Kimi ni Todoke's manga has a conclusive ending that isn't sudden or out of the blue. The narrative progresses smoothly towards its finale, leaving no major loose ends and providing closure for the readers.
I'm not entirely sure specifically as it could be a fan - made or less - known online novel. It might be related to the story in 'Your Name' (kimi no nawa in Japanese), perhaps a novelization or a new take on the story. Maybe it includes more detailed character backstories or different plot developments compared to the movie.
The Kimi ni Todoke anime is generally quite faithful to the manga. There might be some tweaks for the sake of animation or to better fit the pacing, but the core story and characters remain consistent.