One possibility is that Charlie is shocked and immediately starts asking a lot of questions. He might be worried about his daughter being alone with Edward. For example, he could demand to know what their relationship really is.
Another scenario could be that Charlie has suspicions about Edward already. So when he walks in on them, he has this 'I knew it' moment. He could then try to interfere more in Bella's life, perhaps setting some rules about her seeing Edward, thinking he's protecting his daughter from something he doesn't fully understand.
One possible reaction could be shock. Carlisle might be momentarily stunned to see them in an unexpected situation. He could quickly compose himself and offer some words of wisdom or caution. For example, he might remind Edward to be extra careful with Bella considering her human nature.
One possible reason could be that Edward believes Charlie is a threat to Bella in some way that Charlie doesn't realize himself. Maybe Charlie unknowingly gets involved with some dangerous elements, and Edward, with his vampire senses, detects it.
Bella might be extremely embarrassed. She would probably blush and stutter, trying to come up with an explanation for their situation. Since she loves her father and doesn't want to disappoint him, she'd be very flustered.
One possible scenario could be that they travel the world together. They visit different places, experiencing new cultures. Edward could show Bella all the beautiful and historical places he has seen over the years. Another could be that they focus on building a family. They might face challenges like protecting their family from other vampires or supernatural threats. Also, they could be involved in the vampire community more, working towards better relations between different vampire clans.
One possibility is that Renesmee is simply curious. She might ask them what they are doing in a very innocent way. For example, if they are having a private moment, she could break the mood but also add a touch of humor to the situation as they quickly adjust to her presence.
One scenario could be that Edward accidentally endangers Bella's family in the fanfiction. Since Bella is very protective of her family, this could be a major turning point for her feelings towards him. For instance, if his vampire nature attracts some dangerous vampires to Forks and they target her family.
One possible scenario could be that Bella meets a new vampire who has a very different charm from Edward. Maybe this new vampire is more carefree and shows Bella a different side of the vampire world that she becomes attracted to, leading her to cheat in the fanfiction.
Maybe in the fanfiction, Bella wears Edward's clothes as a statement. It could be a way for her to show that she belongs to him in a sense, or that she's part of his world. She might put on his shirt before going to meet his family, for example, as a sign of respect and acceptance of their relationship and his vampire lifestyle.
Together, they would likely try to make Renesmee understand that their relationship is special and that her presence is also special. They might give her a hug or some form of affectionate gesture to show that they are a family unit and that her walking in is just a normal part of family life, even if it was an intrusion on their private time.
For Edward, there's likely a mix of relief and fear. Relief because he's finally expressing his deep love for Bella, but fear because he's exposing his true feelings and also worried about how this will change things. For Bella, she's probably mostly filled with excitement and a bit of shock. The excitement of this new level of intimacy with Edward, and the shock that this moment she might have dreamed of is actually happening.