You can start by looking on fanfiction websites like Archive of Our Own (AO3) or FanFiction.net. Just search for 'Percy Jackson Mrs O'Leary' on their search bars and you'll likely find a variety of stories.
One idea could be that Mrs. O'Leary gets lost in the mortal world and Percy has to find her without using his demigod powers. It would be a fun adventure as he has to rely on his wits and the help of some mortal friends.
A powerful Titan who was previously imprisoned but has now escaped could be a great antagonist. This Titan could have a grudge against Percy for his role in previous battles and sees Mrs. O'Leary as a way to get to him. He could use his own dark magic to try and control Mrs. O'Leary or turn her against Percy.
Another plot could be that Mrs. O'Leary gets lost in the mortal world, and Percy has to find her. Along the way, he discovers that she has made some interesting mortal friends who are in danger because of her association with the demigod world. Percy then has to not only find Mrs. O'Leary but also protect her new friends from the monsters that are after them.
A great alternative would be to write a story about Mrs O'leary's role in her community. Maybe she helps to organize local events, or she is part of a group that is trying to save an old building. This way, it focuses on positive aspects of her character and her place in society.
O'Connor might play the role of a villain in some Percy Jackson fanfiction. They could be jealous of Percy's status as a son of Poseidon and try to undermine him at every turn. They might form alliances with other enemies of Percy, like some of the Titans or monsters. Or they could be a misguided demigod who thinks that the only way to get power is to oppose Percy and his friends.
O'Connor in Percy Jackson fanfiction could be a really interesting character. They could be from a different camp than Camp Half - Blood, like perhaps a secret camp for demigods with some special abilities. Their backstory could involve some mystery related to the gods' past deeds. For example, they could be descendants of a god who was banished long ago and now they're trying to redeem their family's name. They could also be a love interest for one of the main characters, adding a new layer of drama to the story.
Yes, there are some great ones out there. You can find them on various fanfiction websites. Some focus on Percy's new adventures written in the style of George O'Connor, which often bring a fresh perspective to the Percy Jackson world with unique art styles and interpretations if the author is also inspired by O'Connor's illustrative work.
Well, a prevalent theme is forbidden love. Given Percy's world filled with different rules and hierarchies, falling in love with someone who might be from a different group or have different loyalties is a common scenario. Additionally, the idea of soulmates is often explored. Many fanfictions play with the concept that Percy has a destined soulmate and the journey to find or be with that person. There's also the theme of sacrifice in love. Characters might sacrifice their own desires or safety for the one they love, which is very much in line with the heroic nature of the Percy Jackson world.