One common theme is the exploration of power dynamics. Given their different positions in the original story, fanfics often play with how they interact in terms of power.
Well, if Ned married Cersei, it might have changed the course of many events. Their opposing natures and loyalties could have caused chaos within the realm. It could also have affected the relationships of other characters in unexpected ways.
The challenges would be many. Politically, their marriage would be a strange alliance. The Starks and Lannisters have different agendas. Ned would want to rule justly and fairly, while Cersei is only interested in power for herself and her family. Emotionally, they are polar opposites. Ned is a loving father and a man of principle. Cersei is a complex character, often driven by jealousy and greed. Her relationship with Jaime is a major hurdle. And Ned would have a hard time trusting Cersei, given her reputation for underhandedness. Their marriage would be like mixing oil and water in the world of fanfiction.
There's 'The Unlikely Bond' in which the relationship between Ned and Cersei is depicted in a very complex and interesting way. The author delves deep into their personalities and how they might interact given their different backgrounds and motives. It's a really engaging read if you like exploring different character dynamics.
Well, it would be a very different story. Their marriage might force the Starks and Lannisters to work together more closely. But Ned would be constantly aware of Cersei's true nature. He might try to keep her in check, which would make her resent him. And the whole Robert's Rebellion backstory would have a different feel. Since Ned was so close to Robert, his marriage to Cersei would add a strange layer of complexity to that relationship. It could also potentially change the fates of their children, as they would be part of a combined Stark - Lannister family.
In many mainstream comic universes, Ned may or may not appear. It really varies based on the storyline and the creative decisions of the writers and artists.