There's a story titled 'A New Beginning' which focuses on how Harry and Artemis adjust to married life. It shows them building a home together, dealing with family and friends from both of their sides, and how they combine their unique skills to solve problems in their community.
People write it because it's an interesting crossover concept. Combining two very different characters like Harry and Artemis allows for a lot of creative freedom. Writers can explore new relationships, different magical systems interacting, and unique storylines that wouldn't exist in the original universes.
A common theme is the struggle between their different natures. Artemis is a virgin goddess, so the fanfiction often has to deal with how that aspect of her character is reconciled with her being married to Percy. Another theme is the power dynamics, as Artemis is a powerful goddess and Percy is a strong demigod.
Well, in a fanfiction of Artemis and Orion getting married, it could be that they first meet in a very unexpected way. Perhaps Artemis is on a hunt and Orion is lost in the forest. She takes pity on him and helps him find his way. As they spend more time together, they discover a deep connection. Their marriage could then be a grand affair, with all the gods and goddesses invited. But some might come with ulterior motives, creating drama and tension in the story.
In such a fanfiction, the author might focus on the cultural differences between their two characters. Kid Flash is known for his speed and somewhat carefree attitude, while Artemis is more serious and skilled in archery. Their marriage could be a story of two different worlds coming together, and how they learn from each other to make their relationship work.
One common antagonist could be an old enemy of Artemis who doesn't approve of her marrying Percy. This enemy might be a powerful Titan who sees their union as a threat to his plans for revenge against the gods.
One common theme is the struggle against the norms of the Greek pantheon. Since Artemis is a virgin goddess in the original mythology, her marriage to Percy goes against the established rules, so a lot of fanfictions explore the pushback they get from other gods. Another theme is the exploration of their different powers and how they combine. For example, Percy's control over water and Artemis's connection to the moon might be used in unique ways to solve problems in the story.
Well, in this fanfiction, perhaps Artemis is marrying a mortal she has fallen in love with. The story could be about how she tries to balance her life as a goddess with her new role as a wife. She might have to hide her true identity from the mortal world at first, and then as the story progresses, she reveals it, causing a lot of drama and yet also a deeper understanding between her and her new spouse.
One possible plot could be them dealing with a new villain that specifically targets married superheroes. They would have to use their combined skills and the strength of their marriage to overcome the threat.
Yes, there are quite a few. You can start by looking on popular fanfiction websites like Archive of Our Own. Some of these stories might explore their married life, including how they handle their superhero duties while being a married couple.