Can you give some examples of how 'harry potter is an outcast fanfiction' might develop the story?

One way could be that the dialogue of some characters is in one language, say English, while the descriptions or internal thoughts are in another language like German. For example, Harry might be speaking English when interacting with his friends, but when we get a peek into his deeper thoughts about his past or his feelings towards Voldemort, it could be in German.

In this kind of fanfiction, we could see Ron being able to use psychometric magic to understand the history of the Weasley family heirlooms. Maybe he touches an old broomstick and gets visions of all the Weasley siblings who have used it before. Also, Dumbledore could have known about a psychometric spell and used it to study the history of Hogwarts itself, finding out secrets about the founders by touching objects they left behind.

One example could be a fanfiction where Harry uses his invisibility cloak in a more devious way to play pranks on the Slytherins, rather than just for sneaking around. Another might be if Ron uses his chess skills not just for playing the game but to outwit his enemies in a more strategic and underhanded way.

Sure. There could be fanfictions where the author completely misinterprets the relationships between characters. For instance, making Harry and Draco best friends from the start without any of the rivalry and tension that was built in the original series. Then there are those that have really bad pacing. They might spend too much time on unimportant details in the beginning and then rush through the important parts of the story like the climax. And sometimes, the worst ones have a very unoriginal plot. It's just a rehash of the original books but with some minor, uninteresting changes.

He could be creating a dedicated folder on his computer for all his favorite fanfiction stories, which is a simple way of 'nesting'.

Maybe Harry is unable to perform basic spells because he's so coddled that he hasn't had the chance to practice properly. So, his friends have to constantly protect him from minor threats like a pesky pixie.

Sure. One example could be that Harry is able to understand ancient runes and spells without any formal training. He just looks at them and immediately knows what they mean and how to use them. Another could be that he has an inborn ability to communicate with magical creatures in a way that no one else can, and he uses this to gain their help in battles or to solve problems in the wizarding world.

In this fanfiction, Harry could be a player in the sense of being a political player within the wizarding world. He might be secretly forming alliances with different wizarding families to gain power and influence. He uses his status as 'the boy who lived' to his advantage. In relationships, he could be a bit of a heartbreaker. He goes on dates with Hermione, Ginny, and other girls, but is never fully committed, causing some drama and tension among his friends and the girls themselves.

One example could be if there was a lot of bashing of certain characters in the fanfiction, like Ron. Harry might leave the fanfiction because he doesn't agree with the unfair treatment of his friend. He could say something like 'I won't be part of this story that slurs Ron's name for no reason' and then just leave the narrative.

One example could be writing about a character like Snape suddenly having a secret love for Muggle fashion. It's a departure from his usual brooding and strict character in the original, which is quite cheeky. Another might be imagining Harry Potter himself being a bit of a prankster in a way that goes beyond what we saw in the books, like using magic to play elaborate and slightly naughty jokes on the teachers at Hogwarts.