It could be that the 13th Doctor stumbles upon a remnant of Rose's timeline during one of her adventures. Maybe a powerful entity intentionally brings them face to face for a specific purpose.
Sometimes they are. Fanfiction is all about creativity and different authors have different takes. Some stories show them getting married, while others might explore different paths for their relationship.
The fanfiction likely involves a lot of drama and tension. Maybe they have to face their captors' demands and find a way to escape while dealing with Rose's injury.
The two main characters are Rose and the Doctor. Rose is a very relatable character, she's not just along for the ride but actively participates in their adventures. The Doctor, with his centuries - old wisdom and his ability to regenerate, leads the way in their travels. Their dynamic, with Rose asking questions and the Doctor providing answers (sometimes reluctantly), is what makes the fanfiction so engaging.
It could be that the OC and the Doctor have a closer relationship, making Rose feel left out. Or perhaps the OC achieves something that Rose has been striving for.
The main traits of such fanfictions often involve creating steamy and emotional scenes between the two characters. They could also delve into the emotional turmoil and complications of their relationship. Sometimes, they might even introduce alternate universes or unique settings to heighten the drama.