His powers might change in various ways. For instance, if the new world has a different type of magic energy, his spells could be either amplified or weakened. If the new world's magic is more elemental - based, like fire, water, earth, and air, he may need to learn how to adapt his existing spells to work with these elements. Maybe his Patronus charm would take on a different form depending on the new world's magic and its influence on him.
In a new world, Harry's ability to communicate with magical creatures could be affected. If the new world has unique magical creatures with different languages or ways of communication, he'd have to learn new ways to interact with them. Also, his invisibility cloak might not work the same way. The new world could have different laws of physics or magic that interfere with the cloak's function. His ability to use the Marauder's Map might also be limited if the new world has a different layout or magic that confounds the map's magic.
If Harry Potter transfers to Ilvermorny in fanfiction, his relationships would undergo a major shift. At Hogwarts, he had Ron and Hermione, his closest friends. In Ilvermorny, he'd have to find new people to trust. He might be a novelty to the American students, which could attract some and make others jealous. Also, his relationship with authority figures like teachers would be different as they have their own ways of dealing with students in Ilvermorny.
His powers could become a blend of Star Wars and Harry Potter elements. He might be able to use the Force to enhance magic spells or vice versa.
The story would change a great deal. He could use Magneto's powers to enhance his ability to escape from dangerous situations. For instance, if trapped in a room with metal bars, he could simply bend them and get out. His dueling style would also be different. Instead of just using spells, he could incorporate his power over metal to surprise his opponents.
His relationship with the teachers would be quite altered. Professor Snape, for instance, would be even more suspicious of Harry. He might think Harry was using some dark form of magic to gain these ghost powers. On the other hand, Professor Dumbledore would likely be more understanding and see it as another step in Harry's journey. Among his peers, some might envy his powers, while others would be afraid. But his true friends would stay close. His relationship with the ghosts in Hogwarts would also change. Instead of just being an observer, he would be part of their world, and they might treat him differently, either as an equal or as a strange new entity in their midst.
His battles would be different. He could freeze his opponents' wands in ice, rendering them useless.
His view of the universe would expand greatly. He'd realize there are more things out there than just the wizarding world and the Muggle world.
He could form new alliances. Maybe he'd meet characters who are similar to his friends at Hogwarts, or he could befriend those who have powers he's never seen before. His transfer might also bring about a change in his personality. Being in a new and strange place, he may become more adaptable and learn to think outside the box of the magic he's used to. He might even have to hide his identity as a wizard from the new world's inhabitants if they are not familiar with magic.
He'd have to adapt his style. Beauxbatons is known for its elegance and Harry, coming from Hogwarts with its more rugged and diverse ways, would need to tone it down a bit. For example, he'd have to get used to the fancier uniforms and more formal classes.
Well, if Harry Potter has Deadpool's powers, he might become more carefree and irreverent. His traditional sense of duty could be tempered with Deadpool's chaotic nature. He could start cracking more jokes during dangerous situations, like when facing Voldemort. His attitude towards rules might change too, as Deadpool is not one to follow rules strictly.
His view of magic could expand. Anime often has very different interpretations of magic and superpowers. He might start to think more broadly about what magic can do and how it can be used.