Well, perhaps in the fanfiction, Harry adopts Teddy after Teddy has some trouble at Hogwarts. Harry steps in as a father figure. He teaches Teddy advanced magic, things he learned from his own adventures. They might also have a trip around the world of magic together, visiting different magical communities and learning about diverse magic cultures.
Well, perhaps in the fanfiction, Harry adopts Teddy Lupin right after the Battle of Hogwarts. Teddy is just a baby then. Harry, who has lost so many people, sees Teddy as a new beginning. He might face challenges from the wizarding community as some may question his ability to raise Teddy. But Harry, with the help of his friends like Hermione and Ron, overcomes these difficulties and Teddy grows up to be a strong and kind wizard.
Harry's relationship with the Weasley family could grow even deeper. Teddy would be welcomed into the large Weasley clan. Molly Weasley would probably dote on Teddy, cooking his favorite meals. Harry's bond with Neville could also strengthen as they might share their experiences of taking care of the younger generation. And his relationship with the wizarding community as a whole would be seen in a new light, as he is now a father figure.
One challenge could be the Time - Turner rules. If they are using a Time - Turner, they need to be very careful not to break any of the laws regarding time travel. For example, they can't be seen by their past selves or make significant changes that would disrupt the future they come from. Another challenge is the danger of the time period they visit. If they go to a time when Voldemort was active, they are at great risk of being detected by Death Eaters.
There are also other characters like Matt Donovan who, despite being human, has a good heart and knowledge of the town. He could potentially be an ally in a different way, like providing information about the town's non - supernatural aspects. And then there's Alaric Saltzman, who has dealt with all kinds of strange things. His experience and wisdom could be valuable to Harry and Teddy.
In fanfiction, Harry might be protective of Teddy because Teddy is Remus and Tonks' son. Harry has a strong sense of loyalty and he may feel a great responsibility towards Teddy as he lost his parents. Also, Harry has his own experience of growing up without parents, so he doesn't want Teddy to go through any hardships alone.
Luna Lovegood would be a great addition. Her unique perspective on magic could offer new insights to Teddy. Also, Ron could be included as Harry's best friend. His humorous and sometimes clumsy nature could add some light - hearted moments to the story.
One possible reason could be to protect Teddy. Maybe there are some threats in England that Harry wants to keep Teddy away from. For example, there could be some dark wizards or dangerous magical creatures that target Teddy for some reason.
Hermione and Ron would probably be there. They are Harry's best friends, so they might be like aunt and uncle to Teddy. They could help Harry out with raising Teddy, like Hermione giving educational advice.