It could also be that he stumbles upon an unclaimed piece of land during one of his adventures. This land might be enchanted or have some special properties that only he can sense or unlock. And in fanfiction, the author might just want to give Harry a new setting to explore and develop his character further, so they create this land - ownership scenario for him.
Perhaps in some fanfiction, Harry acquires the land through a magical bargain or deal. He might trade some of his magical knowledge or a powerful magical item he has for the land. This could then lead to all sorts of complications and storylines as he has to deal with the terms of the bargain, as well as the new responsibilities that come with land ownership.
One possibility is that it could be an inheritance. Maybe he discovers he has a distant relative who left him a piece of land. Another could be that he is rewarded with land for his heroic deeds. For example, the wizarding community might give him a parcel of land as a token of their gratitude for saving them from Voldemort.
His land ownership in fanfiction might change the power dynamics. If he has a large piece of land, he could have more resources at his disposal. This could attract both friends and foes. For example, some might seek his protection, while others might try to take the land from him for its magical properties or strategic location.
In some fanfictions, it could be a gift from a parallel magical dimension. There could be a race in this other dimension that is very advanced in combining magic and metalwork, and they see Harry as a hero worthy of such a gift. The metal arm could then hold the secrets and powers of that dimension, which Harry has to figure out how to use to save the wizarding world.
It could be an ancient heirloom from a long - lost wizarding family. Maybe it was passed down through generations and finally found its way to Harry.
His metal arm could come from a cursed object that backfired on him. For example, he might have been trying to disarm a powerful dark magic item and it ended up fusing with his arm, turning it into metal. This would then force him to learn how to control the new power within the metal arm.
It depends. In the world of fanfiction, legality can be a bit of a gray area. If Harry created the fanfiction entirely on his own, without using any copyrighted material in an improper way, it could be considered legal. But if he's using elements that are protected by the original Harry Potter copyright in a way that violates the terms, it might not be legal.
The sword might be a gift from a mysterious magical being. This being saw potential in Harry Potter and decided to give him the sword as a tool to help him in his future battles. It could have been enchanted specifically for Harry to face the unique challenges he will encounter.
It could be the result of a dark wizard's experiment gone wrong. Maybe some dark wizard was trying to create a new form of dark magic, and Harry accidentally got caught in the crossfire and ended up with the curse mark.
He could use it to build a magical sanctuary for endangered magical creatures. This would be a place where they could live and breed safely, away from the threats they face in the wizarding world.
Perhaps the tiger is a result of a magical experiment gone wrong. Some wizard was trying to create a new kind of familiar and ended up with a tiger. And then, through some twist of fate, the tiger becomes Harry's familiar. Another possibility is that the tiger was a spirit animal that was drawn to Harry because of his unique magical aura.
It could be from a hidden nest in the Forbidden Forest. There might be a species of snake there that has not been fully discovered by the wizarding community, and Harry somehow forms a bond with one of them.