Well, in such a fanfiction, Harry might be exposed to a whole new world of magical creatures. Newt could teach him about the proper care and understanding of these amazing beasts. Harry would probably grow up with a different set of values and skills compared to his original upbringing in the Dursley's household.
Obviously, Harry would interact a great deal with Newt. But also, they might run into other characters like Hagrid. Hagrid, being the Keeper of Keys and Grounds at Hogwarts and having a great love for magical creatures, would be interested in what Newt and Harry are up to. They could also meet some of Newt's old friends from his adventures in the Fantastic Beasts series.
In a 'Harry Potter adopted by Newt' fanfic, perhaps Newt gets a mysterious message about a powerful but troubled young wizard. When he finds Harry, he realizes that the boy has a connection to the magical creatures world that he doesn't yet understand. Newt takes Harry under his wing. Harry gets to live in Newt's home, which is filled with all sorts of amazing and dangerous creatures. He learns about their habitats, behaviors, and how to communicate with some of them. This knowledge and his bond with Newt could change the way he approaches challenges at Hogwarts and in the wizarding world as a whole.
Harry would probably be more in tune with nature and magical creatures. He'd be less likely to be as reckless as he sometimes is in the original story. Newt's calm and methodical ways would rub off on him. He might be more hesitant to jump into dangerous situations without thinking about the consequences to the surrounding environment and creatures.
Well, in such a fanfiction, Harry might grow up with a deep love and understanding of magical creatures, just like Newt. He could be more in tune with the natural magic in the world outside of Hogwarts' regular curriculum. For example, he might be able to communicate with magical beasts more easily than in the original story.
Another theme is friendship. Despite the age difference and different focuses (Harry on fighting Voldemort and Newt on magical creatures), they can form a unique friendship. Fanfictions explore how they support each other, share their knowledge, and grow together. For example, in some stories, Harry helps Newt with some threats related to dark wizards while Newt teaches Harry about the secrets of magical creatures.
One day in the wizarding world, I decided to act just like Newt Scamander. I grabbed my old, battered suitcase, filled with all sorts of magical creatures. I walked through the Forbidden Forest, looking for injured or lost beasts. Just like Newt, I was calm and gentle when approaching a frightened unicorn. I used my wand to heal its small wound, whispering soothing words. I then released a tiny pixie that I had rescued earlier. It flitted around me, its wings creating a soft, glittery light. I knew that I was on a path similar to Newt's, to protect and understand these wonderful magical creatures.
Their interaction would likely be very interesting. Newt is quite shy and introverted, while Harry is a natural leader. Harry would probably be curious about Newt's magical creatures and Newt would be in awe of Harry's ability to face danger head - on. They might start off a bit awkwardly, but as they get to know each other, they would find common ground in their love for the wizarding world and their desire to protect it from harm.
One common theme is the exploration of different eras of the wizarding world. Since Harry is from a more modern era in the 'Harry Potter' series and Newt is from an earlier time, fanfictions often explore how their different knowledge and experiences of magic can interact. For example, Newt's knowledge of ancient and rare magical creatures can be shared with Harry, who is always eager to learn more about magic.
One of the most popular themes is Newt's exploration of new magical creatures. Fans love to read about his adventures in different parts of the wizarding world as he discovers and studies these amazing beings.