The Padawan could be a young alien from a species not often seen in the Jedi order. Maybe an amphibious species that has a different way of sensing the Force due to their unique physiology. This would make for an interesting dynamic as Anakin would have to adapt his teaching methods.
Another theme is his relationships. Fanfics often focus on his bond with his master, like Obi - Wan, and how that relationship shapes him. Also, his friendships or rivalries with other Padawans are frequently explored.
There's also 'Anakin: The Padawan Years'. This fanfic focuses on his training and how he overcomes various challenges during that time. It's full of action scenes and character development, which makes it a great read.
It could be about Anakin struggling to connect with his new Padawan at first. Maybe the Padawan has a very different approach to the Force than Anakin does. For example, if the Padawan is more in tune with the peaceful aspects of the Force while Anakin is used to a more aggressive style. This difference could lead to some initial clashes between them. But as they go on adventures together, they gradually learn from each other and form a strong bond.
Give the padawan a distinct personality trait. For instance, if the padawan is overly curious, it can lead to all sorts of interesting situations. They might get into trouble by exploring places they're not supposed to.
Well, in theory, it could. Fanfics often like to blend different fictional universes. However, in the official Harry Potter lore, there are no lightsabers. But in a fanfic, an author could come up with some creative magic or a cross - universe event that brings lightsabers into the wizarding world. Maybe a powerful wizard discovers a way to create a weapon similar to a lightsaber using magic and some rare materials.
He could find it during one of his missions. Maybe he's exploring an ancient ruin and stumbles upon the lightsaber. It could be in a chest or just lying there, and Naruto, being curious, picks it up.
Pikachu would probably be very curious. It might zap the lightsaber a bit to see what would happen, and then be in awe of the bright blade. It could also get a bit protective of Ash when he wields the lightsaber, as if it senses the added danger.
Perhaps it's given to him by a mysterious figure. This figure could be from another dimension or a very old ninja who has been in hiding for a long time. They recognize Naruto's potential and power, and decide that he is the one worthy of wielding the black lightsaber. This could be part of a bigger plan to help Naruto defeat a new and powerful enemy that neither the ninja world nor the normal means of combat can handle.