Sure. There are many great 'Twilight' fanfictions that focus on the relationships between Edward, Bella and Carlisle in a non - sexual way. For example, some fanfictions might explore their family dynamics within the Cullen family. They could be about how Carlisle mentors Edward and how Edward's relationship with Bella affects the family as a whole. You can find these on popular fanfiction websites like FanFiction.net by using relevant search terms such as 'Edward Bella Carlisle family relationship Twilight fanfiction'.
Yes. There is a fanfiction that focuses on Carlisle teaching Bella and Edward about the history of their kind. It was really fascinating as it showed how Carlisle's knowledge was passed on and how Edward and Bella reacted to it. Also, there are some that deal with their friendship and loyalty to each other during difficult times in the 'Twilight' world. You just need to look for ones that have a positive and clean story line.
Well, I've read one where they go on a journey together to discover more about their vampire nature in a non - sexual context. It delved into how Carlisle's wisdom influenced Edward and Bella's understanding of their existence. Another one showed them working together to protect the town from some other supernatural threats. These kinds of fanfictions are quite interesting as they focus on the adventure and the bond between the characters rather than inappropriate content.