Your first problem is definitely the easiest. To loop over each line of the file, use while (<>) like so:

open my $outfile, '>', 'out.txt';
while (<>)
{
  print $outfile $_ if /^(?:A id|M X)/;
}
close $outfile;
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Obviously you may need a more rigorous regular expression, but this works for your example data. Your second problem is more difficult, so it'll have to wait for now.

Update: On second glance, your second probem is not well stated. What kind of comparison do you want to do? What should the output look like? Afraid I can't help with a poor problem statement.