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.
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.
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.
In 'Harry and Teddy fanfic', the two main characters are Harry and Teddy. Harry is the one who has been through so much in the wizarding world. He has a sense of responsibility towards Teddy. Teddy is a character full of possibilities. He's the product of a tragic event (his parents' death), and Harry's presence in his life is like a guiding light. Their personalities, Harry's wisdom and Teddy's eagerness to learn, are often explored in these fanfics, which makes for very engaging stories.
She would probably start by teaching Teddy basic magic at home, like how to make a feather float or how to use a simple charm. Since she has her own experiences at Hogwarts, she'd know what's important for a young wizard to learn early on.
One common theme is mentorship turned into something more. Since Harry was a mentor - like figure to Teddy, the fanfictions often explore how that relationship can evolve into a romantic one.