He might like those that show Harry's kindness towards house - elves. Given Kreacher's own status as a house - elf, he would be interested in how Harry is portrayed in relation to his kind in fanfics.
Kreacher may be fond of Harry fanfics that focus on the power of friendship. In the original story, Harry has strong friendships, and if fanfics expand on that in relation to his character, Kreacher, who has seen different aspects of Harry, might be attracted to such stories. Fanfics that also show Harry's growth as a person and a wizard could also be Kreacher's cup of tea, as it gives him more to think about regarding Harry.
Perhaps Kreacher would enjoy fanfics that explore Harry's adventures in the wizarding world from a more personal and emotional perspective. These types of fanfics could give Kreacher a deeper understanding of Harry, which he might like. Also, fanfics that involve Kreacher himself in some positive interactions with Harry could be his favorites.
A fanfic might explore Kreacher's relationship with jewelry in the context of his loyalty to the Black family. He could have been tasked with taking care of certain precious jewelry items over the years. The story could show how he values these items not just for their material worth but also for the family heritage they represent. For instance, a ring that was passed down through generations and how Kreacher ensures its safety during the chaos of the wizarding wars.
Kreacher is a very traditional character. His influence on Harry could mean that Harry is more into the old magic. He might be taught spells and incantations that are not commonly known in modern wizarding society. Also, Kreacher's loyalty to the Black family could make Harry more protective of the remaining members of the family and their heritage.
Yes, he does. Maybe Kreacher, as a character in the Harry Potter world, is intrigued by the different interpretations and adventures of Harry in fanfictions. Fanfics often explore new aspects of characters that might be appealing to him.
One idea for a fanfic is that a new character comes to the wizarding world and has a special piece of jewelry that Kreacher is immediately drawn to. This jewelry has some sort of connection to the house - elf magic. The story could follow how Kreacher and this new character interact, with the jewelry as a focal point. It could lead to Kreacher learning new things about his own kind and his place in the wizarding world, all because of this piece of jewelry.
One common theme is redemption. Kreacher has done some not - so - nice things in the original series, and many fanfictions focus on him finding a way to redeem himself. For example, through helping Harry or the other good characters.
No. Most fanfics tend to focus on positive aspects or different romantic pairings of characters. Depicting a character as abusive is not as common as other themes.
It would be a unique take on the Harry Potter story. Kreacher is a complex character. He could raise Harry in a way that emphasizes self - sufficiency and loyalty to a fault. Harry might not be as eager to jump into the fight against Voldemort as in the original story. Instead, he could be more focused on protecting his own little world created by Kreacher. Also, his magic could develop in a more unorthodox way due to Kreacher's unorthodox teaching methods.
It could be really interesting. Kreacher, being a rather complex and initially prejudiced house - elf, would raise Harry in a very different way from the Dursleys. Harry might grow up with a deep knowledge of the Black family secrets and traditions. He could also be more in tune with the wizarding world's darker elements from a young age.
In fanfiction, Harry and Kreacher could be seen exploring the different terrains of Westeros. Maybe they stumble upon the Iron Islands. Kreacher could be fascinated by the Ironborn way of life while Harry tries to find a way to use their naval power for some greater good. Or they could end up in King's Landing and face the political intrigue there.
I don't think it's a very common type. Most 'Harry Potter' fanfics tend to focus on the magical adventures, the relationships between the main characters like Harry, Ron and Hermione, or exploring different magical elements in the wizarding world. While there are some that might delve into darker themes, the idea of Petunia abusing Harry isn't as mainstream as other topics in the fanfic community.