First, you're not getting 00, you're getting

Missing argument in sprintf at a.pl line 19, <DATAFILE> line 1.
Character:              00
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The root of the problem is

my @list = unpack( 'A' x length($string), $string );
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"A" trims trailing whitespace, and that includes newlines. You want "a".

my @list = unpack( 'a' x length($string), $string );
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or better yet

my @list = unpack( '(a)*', $string );
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So,

while (<DATAFILE>) {
    for my $ch (unpack('(a)*', $_)) {
       printf "Character:\t%s\t%2.2x\n", $ch, ord($ch));
    }
}
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or

while (<DATAFILE>) {
    for my $ord (unpack('C*', $_)) {
       printf "Character:\t%s\t%2.2x\n", chr($ord), $ord);
    }
}
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PS - The name of the encoding is UTF-16LE, not UTF16-LE.