Well, if you keep R-ing TFM, it explains what auto-vivify means, basically it means to spring a new hash/array into existence. Example

$a = {};
warn "exists " if exists $a->{a}{b}{c}{d};
use Data::Dumper;
die Dumper($a);
__END__
$VAR1 = {
          'a' => {
                   'b' => {
                            'c' => {}
                          }
                 }
        };
[download]

The key d in $a->{a}{b}{c}{d} doesn't exist, but look at the magic birth of those hashes ;)

As for Q2, your diagnosis is faulty (whatever the problem is, it's not directly in the snippet you presented). BTW, I find $hash{$key}->() more syntactically appealing ;)