No, it runs SteamOS. Else Pop_OS! is Ubuntu and Nobara is Fedora.
Correct.
I own Steam Deck and I also use Arch as my main desktop distro. While Steam Deck uses Arch as a base, it is slightly tweaked. The file system is read only out of the box and you are supposed to upgrade it together with SteamOS from the Steam settings menu. When connected to monitor and switched to desktop mode, it runs regular KDE desktop. If you want to keep it a vanilla SteamOS (with read only system) but still install apps, you can install flatpaks (for example from KDE application store).