Well, perhaps we can expect to see Harry's moral struggle as he delves into the knowledge of the Unforgivable Curses. It could show his reaction to the dark magic associated with them.
There could also be some within the wizarding community who oppose Harry learning the Unforgivables. They might see it as a sign that he is turning to the dark side and try to stop him, so they could act as antagonists in the story.
Well, we might expect Harry to learn some really cool and powerful new spells. Maybe he'll master some ancient magic that gives him an edge against his enemies.
Well, perhaps we can expect to see Harry Potter in new and creative situations that fanfic writers often come up with. Maybe he'll learn some unique magical skills or have interactions with characters in ways that the original books didn't explore.
Well, perhaps we can expect to see Harry develop new and powerful combat spells. He might face some really tough opponents and use his newly learned battle magic to overcome them.
Well, in this fanfiction, Harry might learn things like how to deal with social situations at Hogwarts that he hadn't fully grasped before. It could show his growth in understanding the magical world's unwritten rules and norms, perhaps through interactions with new characters or facing new challenges that force him to adapt and learn these 'facts of life'.
The 'harry learns the old ways fanfic' is likely centered around Harry's exploration of archaic knowledge or practices. It could be that he discovers an old library filled with dusty tomes that hold the secrets of the old ways. As he reads and learns from these, he might start to incorporate these old ways into his daily life in Hogwarts or his battles against the dark forces. He could learn things like how wizards used to communicate without wands, or ancient forms of defensive magic that have been long forgotten by most in the modern wizarding world.
There could be his arithmancy teacher as a main character too. This teacher might be strict but also very knowledgeable, guiding Harry through the difficult subject.
In the 'Harry Learns Alchemy' fanfic, Harry is the central figure. He is on a journey of learning alchemy. Hermione would be a key character as she is very studious and would be eager to help Harry understand the complex concepts of alchemy. There could be a mysterious old wizard who acts as a mentor to Harry in his alchemical studies. And Ron, as Harry's best friend, would be around, maybe not fully understanding alchemy but being supportive in his own way.
It could be about Harry Potter learning some long - forgotten or lost magical arts. Maybe he discovers ancient spells, potion - making techniques that have been lost for centuries, or unique forms of divination that are no longer practiced in the wizarding world.
It might be a story where Harry delves into the family magic in order to solve some sort of mystery. For example, he could be looking for a way to defeat a new dark force and realizes that the family magic holds the key. He could learn new forms of magic related to protection or divination that are unique to his family.