Harry going back to save Sirius would be a game - changer. First, he'd have to master the Time - Turner better than he did before. He could then go back to the moment right before Sirius was lured into the Department of Mysteries. Harry might use some magic to disguise himself and his friends as Death Eaters to confuse Bellatrix and her cronies. With Sirius alive, Harry would be in a much better mental state. He wouldn't have to deal with the grief of losing Sirius, and Sirius could share his knowledge of the wizarding world and Voldemort with Harry, giving Harry an edge in the battles to come.
If Harry went back to save Sirius, he might first need to figure out the exact time and place of Sirius' encounter with Bellatrix. He could use the Time - Turner more carefully this time. Once there, he could try to prevent Sirius from following Bellatrix into the Department of Mysteries. Maybe he'd bring some backup like Hermione and Ron, but they'd have to be very discreet. This would change the whole course of the story as Sirius was a key figure in Harry's life, and his presence could have influenced Harry's decisions and actions in later events, like the fight against Voldemort.
Well, Harry would need to be extremely cautious when traveling back in time to save Sirius. He'd have to avoid any major disruptions to the timeline that could have unforeseen consequences. One way he could save Sirius is by warning him about the trap Bellatrix was setting. Harry could also try to find a way to get Dumbledore involved earlier. If Sirius was saved, Harry would have a much stronger support system, which would boost his confidence and perhaps make him more powerful in the fight against Voldemort.
One great fanfiction with this plot is 'Time's Redemption'. In it, Harry uses a powerful time - turning spell he discovers in an ancient book. He has to face many challenges in the past, like avoiding detection from the Ministry's time - turner regulations. Another good one is 'Back to Save Sirius'. Here, Harry teams up with Hermione and they use a secret time - travel device left by Dumbledore.
In a time travel scenario, their relationship could become a complex love - hate relationship. Bellatrix may find herself attracted to Harry's courage and determination in a different way than she's used to. Harry, while disgusted by Bellatrix's actions in the original timeline, may start to see a different side of her when they are in a different time period. This would be a very strange and morally ambiguous relationship, full of internal and external conflicts.
Hermione going back in time to stop Voldemort's ascension is a big task. She would need to study the past thoroughly. She might try to change the events that led to Voldemort creating his Horcruxes. For example, she could prevent him from getting the information about Horcruxes in the first place. She could also try to influence the people around young Tom Riddle, like his classmates and teachers, to not be swayed by his charm and instead see his darker side.
The relationship between Harry and Snape would be completely transformed. In the original timeline, Snape had a lot of pent - up anger towards Harry because of his resemblance to James. But if time was turned back, Snape might see Harry as an opportunity to right the wrongs of the past. He could become a mentor to Harry, teaching him advanced potions and dark arts defense in a way that Dumbledore never did. This would also change Harry's perception of Snape from a bitter enemy to a trusted ally.
One great fanfiction could be where Sirius Black travels back in time to prevent his own imprisonment in Azkaban. He might use his knowledge of the future to avoid being framed by Peter Pettigrew. This could change the entire course of the story, as Harry would then have a more stable and present godfather figure in his life from an earlier stage.
Well, at first, Sirius would be in a state of shock and panic. But then he'd have to step up. Their relationship would shift from one of equals (in a sense, as Harry was growing up) to a caretaker - cared - for dynamic. Sirius would have to learn about Harry's likes and dislikes as a baby. He'd sing lullabies to him, comfort him when he cries. This new experience would make their bond stronger in a very different way. Harry might not remember all of it when he's turned back, but there would be a subconscious change in how he feels towards Sirius, a deeper sense of security and love that stems from those baby - days when Sirius was his whole world.
He might use some powerful magic artifacts. For example, the Time - Turner, if he can get his hands on an even more powerful or modified version of it. This could allow him to bypass some of the normal time - travel restrictions.
One popular fanfic with this theme is 'Time's Threads'. In it, Harry and Ginny use a time - turning device to go back and save Sirius. The story is really engaging as it shows their struggle to fit into the past timeline without disrupting too much. They face challenges like dealing with the younger versions of their friends and family.
Their relationship would likely become more complex. Since Harry has only known Lily through memories and stories, actually meeting her in person through time travel would be a shock. Lily would see Harry as a grown man, not the baby she left behind. They might develop a more equal, friend - like relationship as they face the challenges of the time - travel situation together.
On the other hand, if Voldemort travels to the future and sees how much Harry has grown and the resistance against him, he might respect Harry in a strange way. He could see Harry as a worthy adversary, which would change the nature of their enmity. Instead of just hating Harry blindly, he might start to understand him better.