It's fairly common. Fans often look for more content related to their favorite shows. Since 'Attack on Titan' has a large and passionate fan base, there are a lot of fanfics available. 'Aot' fans might watch (read) these fanfics to explore different scenarios that the official story didn't cover. For example, they might want to see how a certain character would react in a different situation or what would happen if a major plot event had a different outcome.
The Sk8 the Infinity manga has indeed finished. It provided a satisfying conclusion to the characters' arcs and the overall storyline. However, fans still discuss and re-read it for the great moments.
Definitely. The anime Sk8 the Infinity originated from a manga. The anime adaptation tries to stay true to the key elements and storylines presented in the manga.
My answer was not accurate. In online novels, SK usually referred to the music group Ska. They were a Japanese music group founded in 2003. Their songs had a wide variety of styles, including pop, rock, electronic, etc. They were very well-known and influential in Japan and around the world.
There could be various fanfictions. Maybe some that focus on alternative endings, like ones where certain characters survive who didn't in the original. For example, a fanfiction where Erwin survives and leads the Scouts in a different way.