For adding a remote that rpm-ostree will use you would add it with the following command
sudo ostree remote add <name of repo> <repository url>. To use ostree commands root privaleges are required.
No there is not bash completion at that level, rpm-ostree does not provide an easy way to list packages contained in a repo, use
ostree remote refs <reponame>. for what it’s worth, I use toolbox and dnf to query the remote for info about packages I’m interested in, and go from there.
Flatpaks are separate from the system they are running on and update with the
flatpak update command. The release cycle of each individual app is the responsibility of the maintainer and is distinct and separate from the system (OS). Rpm-ostree is concerned only with the immutable portion of Silverblue, the core OS image plus whatever package(s) you layer. So
rpm-ostree update would update your base system and layered packages, but not any of your flatpaks.
While there seems to be some thinking that layering of packages is discouraged, the whole intent of rpm-ostree is to provide that flexibility, otherwise you would only need use ostree since it provides no option for layering.
[EDIT]: It appears I was incorrect about bash completion with rpm-ostree, it does indeed have it. As I use zsh, it doesn’t use the bash completion available, this is something I need to correct.