You could focus on a character from one show ending up in the world of the other. Like if one of the Animaniacs gets lost and is found by the Doctor. It could lead to all sorts of interesting plot twists and character interactions.
You could write a story where she has adventures in time and space inspired by her love for the show.
They often feature the familiar characters in new and creative scenarios. The art styles can vary a lot, too, from very close to the original to completely unique.
There's no way for me to know the creator of 'the kicking fan fiction'. Fan fictions are often shared anonymously or by pseudonyms, and this title gives no clues as to who might have written it. It could be a young fan just starting out in the world of fan fiction writing, or it could be an experienced writer exploring a new concept.
You could create stories that explore the characters' backgrounds and motivations in more depth, or imagine new adventures for them.
You could imagine a story where the characters from Mob Psycho 100 find themselves in a house made of cards and have to deal with the unstable structure and its magical implications.
Well, they can be created in various ways. Some authors create them by changing a single key event in the original story. For example, if in the original a character made a certain choice that led to a particular outcome, in the alternate universe, they make a different choice. Others might create an alternate universe by changing the setting, like making a modern - day story take place in a fantasy world instead. It really depends on the creativity of the fan fiction writer.
You can find all sorts of stories. Some might focus on alternate universes or new adventures for the characters. Others could explore deeper relationships between them.
You could have a fanfic where they team up to face a common enemy in a new adventure.
You could imagine a crossover story where the main character from 'The Man from Nowhere' finds himself in the setting of 'Big Valley' and has to face new challenges.
You could write a story where the Doctor and the Muppets team up to save a magical world. It would be full of fun and adventure!