Perhaps there was a dark wizard who was on the loose in the area where Harry lived. This wizard was attacking muggles randomly. Harry, being the Boy Who Lived with an inherent magical power, was able to disrupt the wizard's spell and it backfired, killing the dark wizard. This event could be a huge shock for Harry and his aunt and uncle, who have been trying to suppress his magic all along. It would also make his entry into Hogwarts even more complex as he has already had a major encounter with the dark side of the wizarding world.
In such a fanfiction, Harry could die from an accident. For example, if he discovers magic early and while experimenting without proper guidance, something goes horribly wrong. Maybe he stumbles upon a dangerous magical artifact near his home that has a curse and it kills him before he ever gets to Hogwarts. It would be a very different story from the original, as his death would change the whole dynamic of the wizarding world that we know from the books.
One possibility could be that they meet in a muggle setting, like a local park. Maybe Hermione is reading a book on a bench and Harry, who is always curious, approaches her to ask what she's reading. Another could be that they both end up at the same orphanage for a short time and form a bond over their shared sense of being different from the other kids.
Maybe they attend a pre - Hogwarts magic class together. Harry struggles a bit with some of the advanced spells being taught, and Daphne, though initially a bit aloof, decides to help him. This could start a relationship where they learn from each other, with Daphne learning about Harry's unique experiences outside the wizarding world and Harry getting a better understanding of the pure - blood society through Daphne.
Yes, it is possible. Fanfiction allows for creative reinterpretations of established universes. In this case, imagining Harry Potter as the founder of Hogwarts could lead to some really interesting storylines. It could explore how his modern - day knowledge and experiences would shape the school in its earliest days, perhaps introducing new spells or ways of teaching that are different from what we know of the original founders.
Well, perhaps in the fanfiction Harry finds out that Umbridge has been secretly working for Voldemort all along. He gathers evidence and presents it to Dumbledore and the other teachers. They are shocked and immediately decide that Umbridge can no longer stay at Hogwarts. Harry takes the lead in escorting her out of the school. Or maybe Harry uses his connection with the Order of the Phoenix to get support in getting rid of Umbridge. The Order members come to Hogwarts and together with Harry, they force Umbridge to leave because of her unjust and cruel treatment of the students.
One possible storyline could be that Harry's experience with cancer makes him more resilient. He might have faced his own mortality at a young age, so when he enters the wizarding world, he has a different perspective on danger. For example, he may not be as afraid of Voldemort as others because he has already fought a life - threatening battle with cancer.
Perhaps in the fanfiction, Harry Potter's death occurs because he tries to rewrite a powerful magic spell that goes horribly wrong. He was always known for his bravery and willingness to take risks in the original series, so this could be an extension of that. His death would then be a tragic consequence of his own curiosity and desire to push the boundaries of magic.
One possible scenario could be that Harry is exiled due to false accusations of dark magic. Maybe the Ministry of Magic, fearing his power after the defeat of Voldemort, spreads lies about him being a threat. Another could be that he chooses exile to protect his friends from a new, unknown danger that is targeting him specifically.
One possible scenario could be when Lupin has to leave Hogwarts due to his werewolf secret being revealed more widely. He might cry because he has found a sense of belonging there, with his friends and students. He loves teaching and seeing the young wizards grow, and leaving all that behind is heart - breaking for him.
In another scenario, Harry could expose all of Umbridge's wrongdoings in a very public and embarrassing way. He might use the Marauder's Map to find evidence of her sneaky activities and then present it to the whole school, causing everyone to turn against her and forcing her to leave in disgrace. Harry has a lot of friends who would support him in this, like Hermione and Ron.