Well, in the fanfiction about Voldemort's memories, there could be revelations about his relationships. For example, his connection with his mother, Merope Gaunt. His memories might also show his first encounters with the idea of immortality and how he started to plan his Horcruxes. It can give a deeper understanding of his motives.
Harry might become more cynical. Since Voldemort has seen a lot of dark and cruel things, those memories could taint Harry's view of the wizarding world. He could start to question the motives of people around him more, even those he once trusted, like Dumbledore.
One possible implication is that Harry would gain a deep understanding of Voldemort's motives. He might see how Voldemort's past traumas, like being an orphan and feeling rejected at Hogwarts, led him down the dark path. This could make Harry more empathetic in a strange way, or it could also be a huge burden on him as he has to deal with all the dark and twisted thoughts that Voldemort had.
We can expect to see his early days at Hogwarts. Perhaps there are memories of him being bullied or feeling superior to others. This can explain how his personality developed over time.
He might become more isolated. As his friends might not fully understand what he's going through with these new memories, Harry could start to pull away from them. This would force him to become more self - reliant and introspective. He'd have to dig deep into his own identity to separate himself from Voldemort's influence, which would lead to a more complex and mature Harry.
In the original story, Voldemort doesn't have access to Harry's memories in this way. So in the fanfiction, it creates a completely new scenario. It allows for a different kind of exploration of their relationship. Instead of just their physical and magical battles, we get to see a more psychological interaction.
Harry could become more powerful in a way that scares his friends. Voldemort's training might focus on the Dark Arts, which are powerful but dangerous. This could change Harry's magic style. He may become more solitary as his new skills and knowledge set him apart from his Hogwarts friends who follow a more traditional path of magic.
One interesting plot point could be that Harry discovers a hidden agenda of Voldemort that was unknown to everyone. Maybe there was a part of Voldemort's plan that was so well - hidden that only by having his memories can Harry find out. This could lead to a new race against time to stop something that Voldemort had set in motion long ago.
It's possible. In the realm of fanfiction, the imagination knows no bounds. Writers might come up with such a scenario for various reasons, perhaps to explore a different side of the characters' relationships. But it's not a common or mainstream concept within the Harry Potter fanfiction community, as it goes against the typical character dynamics we expect from the series.
In many fanfictions, Harry Potter squinting at Voldemort could be a sign of intense focus. It might be that Harry is trying to read Voldemort's next move, or perhaps he's looking for some sign of weakness. For example, in some stories, Harry's squinting could be related to his newfound magical abilities that he's using to analyze Voldemort's magic signature.