Does that command work at all? I would have though that specifying --root /mnt/disk also sets the root for when the config files is. i.e. that should mean that --config argument now looks in /mnt/disk/mnt/disk/etc/pacman.conf?

For testing purposes we can try this command and watch the output:
# pacman --debug --root /mnt/disk --dbpath /var/lib/pacman -Q | less

Then you can include also --cachedir, --config, --logfile with the values we want and watch the output.

We always get this line:

debug: config: finished parsing /etc/pacman.d/mirrorlist

So mirrorlist file is never changed.

-1 from me.

First, --config is completely different than any of the rest of the options. Unfortunately this is not documented clearly enough in the manpage, but notice the wording under --root:

-r, --root <'path'>
Specify an alternative installation root (default is ‘`/''). This should not be used as a way to install software into
``/usr/local’' instead of “/usr”. This option is used if you want to install a package on a temporary mounted partition which is
"owned" by another system. NOTE: if database path or logfile are not specified on either the command line or in pacman.conf(5),
their default location will be inside this root path.

It does *not* include --config, and for good reason- the config file path has to be done before anything else, and thus can't use information from anywhere else. Why would I point it to a config in one place and expect it to go chasing files elsewhere? What do I do if I specify a root on the command line vs. in the config file? Which do I prefer over the other? What if an Include comes both before and after a DBPath option?

The only thing that needs doing here is better documentation.

* Why would I point it to a config in one place and expect it to go chasing files elsewhere? *
This is the point! But is what pacman is doing actually!

If I try to install something in a second disk(other mountpoint/other system), with a config file in that second disk, why is pacman using mirrorlist from the first disk?

Because pacman doesn't care what a disk is. It does exactly what you tell it to with the paths it has available. While I understand your confusion, like I said, that can be solved with better documentation.

You failed to address any of the "when do we resolve path X" questions I asked in my previous comment, so without doing that, I don't know what you want. Patches welcome.

As of commit fae33a1faf3f94ea46049664ef483b2a3e0d3f01 this use case is served by --sysroot.