Yes, it is. As a 'Code Geass' fan, it gives you more content related to the series. You get to explore the story further and might discover new aspects of the characters and the world.
Code Geass did start as a manga. However, its anime version became even more widely known and beloved. The manga provided the foundation for the rich story and characters that were further developed in the anime.
Code Geass started as an anime. The manga was based on the anime's success and came after to expand the story for fans. Some elements might differ between the two, but the anime was the original form.
The 'Code Geass 5 Year Fanfic' might expand on the original world - building by delving deeper into the politics of the different nations. For example, it could explore how Britannia's rule has changed over the five years, whether there are new rebellions brewing in different regions. It may also focus on the economic aspects. Maybe some regions are suffering more due to Britannia's policies, and this leads to new forms of resistance.
In most cases, yes. Fanfiction is a form of creative work by fans, and as long as it doesn't violate any copyright laws in a major way (like using the original work for commercial gain without permission), it's generally okay to view. However, the legality can get a bit murky in some situations, for example, if the fanfiction contains elements that are too close to the original's plot in a way that could be seen as copyright infringement.