You can try searching on popular fanfiction websites like Archive of Our Own (AO3). They have a large collection of fanfics, and by using the relevant tags such as 'Fem Harry Potter' and 'Adopted by Loki', you might be able to find the ones you're interested in.
Well, it could start with Loki somehow coming across Fem Harry Potter in a dire situation in the wizarding world. Maybe she's being persecuted because of her femininity and her connection to Voldemort in a different way than in the original story. Loki, being the complex character he is, decides to take her under his wing, perhaps seeing some potential in her that others don't.
If Harry Potter was adopted by Loki in fanfiction, his life would be full of chaos. Loki is a trickster god. Harry might learn all kinds of magic and mischief that are far from the normal wizarding world. He could be exposed to Asgardian magic which is different from Hogwarts magic. And Loki's unpredictable nature would constantly keep Harry on his toes, making his life a wild adventure.
In this fanfiction scenario, their relationship could start off rocky. Loki is used to his own ways and Harry has his own set of values from the wizarding world. However, as time goes on, they could grow to understand each other. Loki might see Harry as a tool at first, but gradually develop a sense of fatherly love. Harry would come to respect Loki's power and wisdom, and they could become a formidable duo, with Harry learning Loki's tricks and Loki learning about the magic of the wizarding world.
Well, in the world of fanfiction, just about any concept can be explored, so it's highly likely that there is a 'harry potter is loki reincarnated' fanfiction. Writers love to mash up different universes and characters. This particular concept could bring in elements of Loki's mischievous nature into Harry's character, creating a whole new set of adventures and challenges for him in the Hogwarts setting.
Loki is a powerful Asgardian with abilities that are more in the realm of the supernatural in a different way than Harry's magic. But Harry has a strong will and has faced some extremely tough opponents. In a fanfiction, if the writer decides to give Harry access to some of the most powerful and ancient magic in the wizarding world, he could be more powerful. For example, if he could use the magic that created the Hogwarts itself, he might be able to stop Loki quite effectively. Also, Harry has the support of his friends and the entire wizarding community behind him, which could give him an edge in power.
It's hard to say. Loki has a wide range of magical abilities from Asgard. He can shape - shift, create illusions, and has a certain level of telekinesis. However, Harry Potter has the power of love and friendship on his side, which has proven to be a very strong force in his world. Also, Harry is very skilled at defensive and offensive magic within the wizarding world. So it really depends on the situation.
Yes, there are likely to be some. Fanfiction is a vast world and many creative writers combine different fictional universes like Harry Potter and Norse mythology. You can try searching on popular fanfiction websites such as Archive of Our Own or Fanfiction.net.
One idea could be that Loki, being the mischievous character he is, finds his way into the wizarding world of Harry Potter. He could start causing chaos in Hogwarts, perhaps by disguising himself as a student or a professor and playing pranks that are far more elaborate than those of the Weasley twins. For example, he might turn the entire Great Hall into an ice rink during breakfast time.
Loki's mischievous personality could make Harry more adventurous. Harry might start to take more risks in his magical studies and in facing Voldemort. For example, he could be more willing to try out untested spells or strategies.