Of your test cases, I think this one is the most important to understand:

use strict;
use warnings;

my @A = (0) x 20;

PrintA(); 
ChangeArray5(\@A);
PrintA(); 

sub ChangeArray5
{
  my $B = shift;       # I don't understand this, but it works :P

  foreach my $X (@$B)
  {
    $X = 5;
  }
}

sub PrintA { print "\n".join('', @A); }

__END__
Prints:

00000000000000000000
55555555555555555555
[download]

$B is a reference to the @A array. When it is de-referenced, you get an alias to the original array - not a copy of the original array - you are accessing the original array itself. Huge arrays can be passed to subroutines and modified in this way.

If you want to operate upon a copy, then my @copy = (@$B) and iterate over @copy.
I guess as a side note, $a and $b have special meanings in Perl. I wouldn't use $A or $B due to possible confusion.