No, it is not appropriate. Creating or distributing sexual fanfiction involving underage or fictional characters in a sexual context is unethical and often violates the terms of use of various platforms. Such content can also be considered a form of inappropriate objectification.
Well, 'shoto todoroki abused fanfiction' might be centered around the idea of taking the character Shoto Todoroki from the original source material and putting him in an abusive context. This could be physical, emotional, or psychological abuse. Some writers may use this as a means to develop the character further, to show his strength in overcoming such difficult situations, or it could be a way to delve into the darker sides of the fictional world in which he exists. It could also be a form of expressing the writer's own creativity and interpretation of the character's potential experiences.
I'm not sure if it's common. It depends on the popularity of the character Shoto Todoroki in the fanfiction community and the prevalence of darker, more angsty themes. Some fans might be interested in exploring such complex and difficult topics, while others might prefer more positive or light - hearted fanfiction about the character.
Family is a common theme. Since Shoto has a complex family situation, fanfictions often explore how his family members interact with him as a baby. For example, how his father might view a baby Shoto with his powerful quirk.
Love and romance are also prevalent. The female character might fall in love with Shoto as she gets to know his kind heart beneath his cold exterior. This can lead to a lot of sweet and sometimes angsty moments as they navigate their relationship.
The main differences are in their expressions and some minor details of personality. In the manga, Deku might seem a bit more intense, while in the anime, he's sometimes presented a bit softer.
In 'deku meets future deku fanfiction', perhaps the future Deku warns the present one about upcoming threats. He could tell him about villains he'll face in the future and how to defeat them. This would give the present Deku an edge in his battles and also in his growth as a hero.