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.
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.
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.
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.
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.
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.
Fanfiction often gives Christine more agency. In the original, she can seem a bit passive at times. But in fanfiction, like 'Christine's New Path', she might take control of her own destiny and not just be the object of the Phantom and Raoul's affections.
One possible fanfic could be about the Phantom's unrequited love for Christine. He might express his love in a more desperate and passionate way than in the original story, perhaps through a series of secret letters or gifts that he leaves for her. Christine, on the other hand, could be conflicted between her fear of the Phantom and her growing understanding of his tortured soul.
The fanfic could take a darker turn. What if the Phantom's 'I love you' was more of an obsession? He could kidnap Christine again, but this time, instead of scaring her, he tries to show her the world he has created for them. Christine has to fight between her sense of self - preservation and her growing pity for the Phantom.