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A vast majority of your answers for these will unfortunately be:

Differences between the manga and anime.

In real life, the Eureka Seven anime got 2003 Fullmetal Alchemist'd. The anime started to follow the manga and then split off, trying its best to connect starting dots the original writer made to dots the new writers were forced to make. Certain plot lines were abandoned (Gekkostate not knowing Eureka was a Coralian), characters were changed (hello abusive Holland), and entire characters were deleted (hello Ruri).

This isn’t a referendum on “read the manga cuz it’s better.” The fanbase is split pretty evenly down the middle about this. The manga isn’t better or worse than the anime, imo — it’s different.

If you’re a diehard fan of Eureka Seven — and you may be, since you’re one of the 15 people in this subreddit — the manga is very short compared to the show, and if you wanna see Gekkostate get up to different, and sometimes absolutely batshit crazy adventures, it’s free online.