I'm not sure exactly as I haven't read it, but often in novels with such a title, there could be a central character who is trying to hold a family or a group together.
Another theme might be loyalty. The title 'the tie that binds' gives an impression of something that holds people or ideas together, which could be loyalty among characters in the story.
Yes, there are quite a few. You can start by looking on popular fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Harry Potter Binds Demons' in their search bars, and you'll likely find a variety of stories with different plotlines and interpretations.
One common theme could be the struggle between good and evil. Since demons are often associated with evil, Harry and his friends would be fighting to keep the demons in check. Another theme might be the discovery of new magic. Binding demons is not a common practice in the original Harry Potter books, so exploring this new type of magic could be a big part of the stories.
One possible plot could be that Harry, perhaps in a search for power or knowledge, binds the succubus. But then he has to constantly battle her wiles and temptations as she tries to break free. He might use magic he's learned at Hogwarts to keep her in check.
Well, it could be that Harry, in this fanfic, discovers a way to bind the succubus familiar through some ancient magic he stumbles upon. Maybe he needs its powers for a particular task, like fighting a new dark force in the wizarding world.
There could be a new, powerful dark wizard or witch who has emerged. This character might not be directly related to Voldemort but has their own reasons for wanting to bind Harry. They could see Harry as a threat to their own rise to power in the wizarding world, so they take this extreme step to incapacitate him.
Sakura might have a hidden jutsu or power that she has not yet fully explored. In this dire situation, she could tap into this unknown ability to break free from the snakes. For example, she could have some latent chakra - based power that she discovers can repel or dissolve the snakes binding her.
One interesting storyline could be a magical adventure where the three of them team up to solve a mystery in the wizarding world. For example, they might be on a quest to find a lost magical artifact that has the power to save Hogwarts from a new dark threat. Hermione's intelligence, Fleur's charm, and Harry's courage would all play crucial roles in this adventure.