You already answered the question by yourself: chroot is how you run stuff inside another installation, and this includes package manager commands. Pacman does have its own option to work on an alternative root (-r), but it's not fundamentally different.

The easiest approach is to ls /mnt/var/lib/pacman/local. Each installed package's metadata is stored as a separate directory; cut off the last two fields to get just the package name.

Pacman does not distinguish AUR packages from other types of packages. Once it's installed, it's always a "local" package whether it came from a repo or from your own makepkg.

You already answered the question by yourself: chroot is how you run stuff inside another installation, and this includes package manager commands. 

Pacman does have its own option to work on an alternative root: -r, e.g. pacman -Qr <dir>, but it's not fundamentally different.

The easiest approach is to ls /mnt/var/lib/pacman/local. Each installed package's metadata is stored as a separate directory which is named after that package; cut off the last two fields to get just the pkgname.

Pacman does not distinguish AUR packages from other types of packages. Once it's installed, it's always a "local" package whether it came from a repo or from your own makepkg.