One great 'Harry ends up in past with Teddy' fanfiction is 'Time's Twist'. In it, Harry's journey in the past with Teddy leads to some interesting changes in the wizarding world's history. They form a strong bond and together face many challenges that were previously unknown in the original timeline.
In most of these fanfictions, once Harry and Teddy are in the past, they first have to figure out how to blend in. Teddy, being younger, might rely on Harry a lot. Harry, with his knowledge from the future, will start to make decisions that could change the course of history. For example, he might introduce new magical concepts earlier or prevent certain dark wizards from rising to power. As the story progresses, their relationship deepens as they face challenges together, like dealing with the suspicions of other wizards in the past who notice their strange behavior or knowledge. And there are often emotional moments where Harry reflects on his own past and how this new experience is changing his perspective on things.
Definitely his professors when they were younger. For example, Snape as a student. This would be a strange interaction considering their relationship in Harry's own time. He could also meet Hagrid when he was just starting out at Hogwarts. And there's a good chance he'd run into Sirius and Remus during their school days, and perhaps form new friendships or alliances with them in the past.
One possibility is that Harry would use this opportunity to change certain events in the past that had a negative impact on the baby or its family. He could also form a special bond with the baby. Maybe he'd introduce the baby to some of his friends from his own time who are also in the past now. This could create a whole new set of relationships and storylines in the fanfiction.
Well, he might try to expose Voldemort earlier in his rise to power. Harry could use his knowledge of Voldemort's Horcruxes to start looking for them right away. Also, in the past, he could form new alliances. Maybe he teams up with some of the older generations of wizards and witches who were previously unaware of Voldemort's true intentions. And his presence in the past could cause a stir in the wizarding world as people try to figure out who this mysterious boy is with such strange knowledge.
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.
Well, the storyline could change in many ways. For example, if Naruto goes back in time, he might prevent some of the tragedies that happened in the original story. He could stop the Uchiha massacre, which would completely change Sasuke's story arc. Also, he might be able to train with the earlier versions of his teachers and learn new jutsu much earlier, making him even more powerful in the future timeline.