Assuming 'apart' means the 2nd question isn't also a joke, yes, the dot is one of the command prefixes.

It works on built-in command directly, though there is an exception:

//say test $true
//echo test $show
//.say test $true
//.echo test $show
both behave identically, but same doesn't happen with /me.

While it works on build-in commands used by your custom alias, it doesn't mute the echoes displayed by your alias unless the code specifically check $show. i.e. "if ($show) echo -s message"

But be aware the $show seems to be inherited from one custom alias to another:

alias foo {
echo -a foo $show
alias foo2 {
echo -a foo2 $show
var -s %a test
set -su %a test

If you run: /foo
then both messages displayed by foo2 display $true or $false depending on whether foo2 was called using the dot prefix.
However, if you run: /.foo
then foo2 always inherits the $false from how foo was called, even when foo2 was called without it. The example shows this also prevents /var -s and /set -s from displaying their messages in both the latter cases, because it also is inheriting the $show setting from the first alias.