One interesting plot could be Harry going back in time to prevent the death of his parents. He might use his knowledge of future events to outwit Voldemort before he becomes too powerful. Another could be Harry traveling back to his first year at Hogwarts and changing how he interacted with certain characters like Snape, which could lead to a different dynamic between them throughout the series.
Hermione is often one of the most common characters. Since she's Harry's best friend and very intelligent, she's likely to be involved in any time - traveling adventures. Another is Dumbledore. Harry might seek his guidance in the past, and Dumbledore's wisdom would be invaluable. Also, Sirius Black could be a character Harry interacts with, especially if he wants to change the events that led to Sirius' death.
Ron is also a common character. He could provide the comic relief as well as be part of the adventure with Harry. Dumbledore might also show up as he is the wise mentor figure. Harry might seek his advice on how to handle the changes he wants to make in the past without disrupting the future too much.
One interesting plotline could be Harry going back in time to prevent certain deaths, like Sirius Black's. He might use his knowledge of future events to change the course of history and save his loved ones.
She could meet the founders of Hogwarts. Imagine Hermione having a conversation with Rowena Ravenclaw about the importance of knowledge and wisdom. She might also meet Godric Gryffindor and learn about the true meaning of courage from him. Another person she could meet is Salazar Slytherin. It would be very interesting to see how she would interact with him, given his views on blood purity.
One possible fanfiction could be about Harry Potter accidentally stumbling upon a time - turning device in Hogwarts and ending up in the 1940s. There, he might meet the young versions of his professors, like Dumbledore, and get involved in the events that were shaping the wizarding world at that time, such as the rise of Grindelwald.
I can recommend you a novel that travels back to ancient times. It's called " The Peerless Beauty in Ancient Times." This novel was about a modern girl who accidentally traveled to ancient times and became a beautiful woman. She experienced all kinds of tests and challenges in ancient life and finally obtained her own happiness and achievements. The plot of the novel is full of twists and turns, the characters are vivid, and the language is beautiful. It is the best choice for you to read.
He could meet his future children, if he has any. They would likely be powerful wizards or witches with their own adventures. Also, he might run into the future versions of Hermione and Ron. They would probably be in important positions in the wizarding world, like Hermione might be a headmistress at Hogwarts or something.
Definitely Hermione. Since she's Harry's closest friend and very intelligent, she would be deeply involved in any changes Harry tries to make. Also, Snape. Harry's actions in the past could completely change his relationship with Snape. And of course, Voldemort. If Harry goes back far enough, he could potentially stop Voldemort's transformation into the evil wizard he became.
Harry could face the problem of balancing his knowledge from the future and not revealing too much. There could also be issues with dealing with younger versions of his friends and enemies. And, of course, he'd have to navigate the magical world of the second year without raising too many suspicions.