I will admit from the start ... interested to find the filename printed instead of the expected "0".

Dang, dat don soun like no good english :D (I actually don't know, just sounds, well, interesting to me :)

FWIW, its all good, at least you're trying , to learn (as opposed just finish some program) :)

a) What is the actual purpose of the special scalar variable, $0, which holds the filename of the script (I have read perlvar, but still don't understand the significance);

That is the purpose, the hold the name of the script (hey, people want to know what it is, if they can )

b) Did I not get a warning about the undeclared variable because it was being assigned to a declared variable, or did I not get it because it was a special variable such as $_ and why should this be the case; and,

What undeclared variable, $0? Perl declares/defines/initializes $0 for you, its a pre-defined global variable

c) Did the count iterate to 1..9 because the special scalar variable, $0, was treated as zero due to the numeric lt (<) operator? Or, in other words, how was the condition able to be evaluated if it did not conform to initial expectations by being non-numeric?

This is equivalent to that for loop

#!/usr/bin/perl --
use strict; use warnings;
{
    my $count = $0; 
LOOOOOP: while(1){
        print "$count\n";
        if( not ( $count < 10 ) ){ 
            last LOOOOOP ;
        } else {
            $count++;
        }
    }
    undef $count;
}
__END__
$ perl junk
junk
Argument "junk" isn't numeric in numeric lt (<) at junk line 7.
1
2
3
4
5
6
7
8
9
10
[download]

Do you get it now?

Try another

#!/usr/bin/perl --
use strict; use warnings;
{
    my $count = $0; 
LOOOOOP: {
        print "$count\n";
        if( not ( $count < 10 ) ){ 
            goto NO_MORE_LOOP;
        } else {
            $count++;
            goto LOOOOOP;
        }
    }
NO_MORE_LOOP:
    undef $count;
}
[download]

I apologise in advance for the "baby Perl" questions.

This free book covers this level of experience :) http://learn.perl.org/books/beginning-perl/