One interesting fanfiction could be where Bella has some unique powers that Aro is extremely interested in. In this type of story, it might explore how their relationship changes due to her powers and how the Volturi react as a whole. Another could be a time - travel fanfiction where Bella goes back in time and meets a younger Aro, changing the course of vampire - human relations in the Twilight universe. There are also fanfictions that focus on a more romantic relationship between them, defying the typical Bella - Edward dynamic we see in the original series.
In certain fanfictions, their interaction is more of a romantic nature. Aro may be attracted to Bella's strong will and her different way of thinking. Bella might initially be repulsed by Aro but then slowly starts to see his good side. Their relationship in these fanfictions develops over time, often with many obstacles in the way, such as the Cullens' disapproval and the Volturi's own strict rules about relationships.
Fanfiction.net could also be a good place to look. However, the tagging system there might not be as detailed as AO3. So you may need to do a bit more sifting through the results. Sometimes, Tumblr blogs dedicated to fanfiction might also reblog or recommend such stories.
One common theme is the clash of two different magical worlds. Harry Potter's world of spells and wands meets the Twilight world of vampires with unique powers. Another theme could be the relationship between the female Harry Potter and Aro Volturi. It might explore how they interact, given their different personalities and power dynamics.
They might be either amused or offended. The Volturi are very traditional and strict in the Twilight universe. Fanfiction often takes creative liberties that could go against their values.
Power is a common theme. The Volturi are a powerful vampire coven, so fanfictions often explore how they use and maintain their power. For example, in many stories, they deal with threats to their authority.
Sure. 'Aro's Redemption' is a great one. It explores Aro's character in a different light, showing his more complex side rather than just the villainous one we often see in the original story.