Midoriya's friends like Uraraka and Iida would be extremely worried. They would immediately start looking for him. Uraraka might use her quirk to search in the air, while Iida would lead the ground search with his speed. Bakugo, on the other hand, would be furious. He would probably go on a solo mission to find Deku and take on Todoroki without hesitation.
I haven't come across one, but you could try looking on specialized comic websites or social media groups focused on comics. Maybe someone there knows if such a comic exists.
No, it's not appropriate. Deku is a character with his own depth, goals, and story within the MHA universe. Fanfic should aim to explore his hero journey, his relationships in terms of mutual respect and support, not create content that focuses on inappropriate or disrespectful ideas like this.
A 'villain deku x villain todoroki fanfiction' might focus on their backstories that led them to become villains. It could be that they were both wronged by the hero system in some way. Deku might have been rejected too many times or faced unfair treatment, and Todoroki could have some family - related issues that pushed him to the dark side. The story could then show how they form an alliance and start their villainous journey together.
One great 'Best villain Deku fanfic' is 'Villainous Deku: The Dark Ascent'. It shows Deku turning to the dark side in a very believable way. The author does an excellent job of portraying his inner turmoil and the reasons behind his transformation. Another one could be 'Deku's Villainous Reign' which has some really intense action scenes where villain Deku battles against his former friends. It's a thrilling read.
Definitely not. Deku's character arc in the manga is centered around his growth and development as a hero. There are challenges and difficulties, but he never turns to the dark side.