Coincidentally, I am in the middle of working with gzipped logs myself. Perl, by itself, does not "understand" gzip files. You must make it understand by using Compress::Zlib or IO::Zlib. I prefer the latter, as it emulates the IO::* interface and makes your code a lot easier to work with. That said, you can do something like this:

use strict;
use warnings;

use IO::Zlib; # also uses Compress::Zlib

my @hostnames = qw(baloo beast belle chip cogsworth lefou potts);
my $timestamp = $ARGV[0];
foreach my $host ( @hostnames ) {
  my $logpath = "/archive/$host/www/logs/access_log.$timestamp";
  my $fh = IO::Zlib->new($logpath, "r");
  die "Cannot open $logpath: $!" if !$fh;
# Probably good to check Compress::Zlib::gzerrno, too.
  while ( <$fh> ) {
    # do text processing here
  };
  $fh->close;
}
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As for your third question, I'm not quite sure what you mean. I tend to use Date::Manip for all of my happy-fun date processing.