One common theme is redemption. The Phantom, often seen as a tragic figure, may seek redemption through his relationship with Christine. He might change his ways and learn to love in a more positive and selfless manner.
The relationship can start with mystery. For example, Christine could hear the Phantom's voice in the opera house but not see him at first. Then, as she gets closer to uncovering his identity, there's a sense of both fear and attraction. This could lead to a series of meetings where they talk about music, and Christine slowly begins to see the man behind the mask, both literally and metaphorically.
Fanfiction about them often delves into the unspoken emotions. It can show the Phantom's vulnerability more clearly. Maybe in a fanfic, he reveals his past traumas to Christine, which deepens their bond.
Yes, there are many. Some fanfictions focus on their emotional connection, like how they first met and the gradual development of their understanding and respect for each other. For example, there are stories where Christine discovers the Phantom's tragic past and tries to heal his inner wounds through friendship.
Another possible antagonist could be the new opera managers. They could be trying to use Christine's disappearance to their advantage, perhaps by spreading rumors that she has run away with a lover to create a scandal and boost ticket sales. They might also try to stop Raoul from searching for her, seeing it as bad for business.
There are many positive alternatives. For example, you can explore fanfiction that focuses on the deep emotional bond between Christine and the Phantom in a more respectful way. Some fanfictions might explore their relationship in a platonic or romantic but chaste sense, delving into their shared love for music and the opera house.
I'm not aware of any such fanfiction. Fanfiction should ideally be in line with ethical and moral standards, and creating 'naughty' or inappropriate fanfiction is not acceptable behavior in the fan community.
One popular 'Christine and Phantom' fanfiction might be those that explore their relationship in an alternate universe. For example, a story where they are able to communicate more freely without the constraints of the original story's setting. Another could be a fanfiction that delves deeper into the Phantom's past and how it affects his relationship with Christine. There are also fanfictions that might give a happier ending to their story, different from the somewhat tragic end in the original work.