I'm not sure specifically as it could vary greatly. Fanfics are often based on existing stories or characters, so it might be about a character with some sort of power and the events that unfold around that power. Maybe it's a warning to others about the might of a particular character in the fanfic's universe.
I really don't know the main characters in 'beware my power fanfic'. It could be that the main character is the one who possesses the power that others need to beware of. Or perhaps there are multiple main characters, like a group of friends or allies who are either trying to control or oppose the character with the power.
One should beware of the complex relationships between the characters. In many novels with brothers as central elements, their relationships can be full of jealousy, rivalry, and hidden agendas.
"My Power is Infinite" was a fantasy/modern magic novel. The story was set in a world where Reiki was recovering, beasts were rampaging, and superpowers were rising. The protagonist could copy other people's abilities, including controlling lightning, controlling fire, transforming into a giant, regrowing broken limbs, teleportation, telepathy, and so on. Other than that, there were also some similar novels recommended, such as Book of Troubled Times, Spirit Realm Walker, Tang People's Table, King of Imperial Beasts, and so on. However, the search results didn't provide any information about the plot and author of "My Esper Ability is Infinite."
Well, perhaps it's a warning within the context of these farm stories. Maybe the farm is near a forest where bears roam, and the 'little box of farm stories' contains tales about the potential danger that bears pose to the farm or the people on it. So it's like a cautionary note for those who are about to read or listen to the stories.
In many 'beware of the dog' stories, it can also be about a dog that is protecting something valuable. Say, on a farm where the dog is guarding the livestock. The full story might include how the dog was trained to be protective, what signs it gives before it attacks if it feels threatened. It could also involve the relationship between the dog and its owner, and how the owner manages the dog's protective nature to avoid unnecessary harm to others.
There's no way to tell who created the 'beware game story' without more context. It could be an indie developer who made a small, niche game with this type of story, or it could be a large game studio that incorporated a 'beware' - themed story into one of their big - budget titles.
Well, the 'beware game story' could refer to a narrative in a game that has elements of caution. Maybe it's a horror - game story where the player has to beware of the monsters lurking in the dark. For example, in a survival horror game, the story might revolve around a character who has to beware of limited resources while trying to escape from a haunted place.