I don't know why you're using select for this problem. If you were to use select, you'd have

use strict;
use warnings;

use IO::Handle qw( );         # For autoflush.
use IO::Select qw( );
use IPC::Open3 qw( open3 );
use Symbol     qw( gensym );

use constant BLK_SIZE => 64*1024;

my $pid = open3(
   my $stdin_fh  = gensym(),
   my $stdout_fh = gensym(),
   my $stderr_fh = gensym(),
   'server.pl',
);

$stdin_fh->autoflush(1);

my $stdin_buf  = '';
my $stdout_buf = '';
my $stderr_buf = '';

my $writers = IO::Select->new();
my $readers = IO::Select->new($stdout_fh, $stderr_fh);


my %answers = (
   "What is your name?"           => 'ikegami',
   "What is your mission?"        => 'To become the King of Halloween'
+,
   "What is your favorite color?" => 'orange',
);

while ($readers->count()) {
   my ($ready_readers, $ready_writers) = IO::Select::select($readers, 
+$writers, undef);

   foreach my $fh (@$ready_readers) {
      if ($fh == $stdout_fh) {
         my $rv = sysread($fh, $stdout_buf, BLK_SIZE, length($stdout_b
+uf));

         if (!defined($rv)) {
            $readers->remove($fh);
            # ...[ Do something in response to error from sysread. ]..
+.
         }

         elsif (!$rv) {
            $readers->remove($fh);
            # ...[ Do something in response to EOF from sysread. ]...
         }

         else {
            while ($stdout_buf =~ s/(.*)\n//) {
               my $query = $1;
               if ($query =~ /Have a nice day!\z/) {
                  $readers->remove($fh);
                  print("$query\n");
               } elsif ($answers{$query}) {
                  $stdin_buf .= "$answers{$query}\n";
                  $writers->add($stdin_fh);
               } else {
                  # ...[ Do something with unrecognised output from ST
+DIN. ]...
               }
            }
         }
      }

      if ($fh == $stderr_fh) {
         my $rv = sysread($fh, $stderr_buf, BLK_SIZE, length($stderr_b
+uf));

         if (!defined($rv)) {
            $readers->remove($fh);
            # ...[ Do something in response to error from sysread. ]..
+.
         }

         elsif (!$rv) {
            $readers->remove($fh);
            # ...[ Do something in response to EOF from sysread. ]...
         }

         else {
            # ...[ Do something in response to output to STDERR. ]...
         }
      }
   }


   foreach my $fh (@$ready_writers) {
      if (length($stdin_buf)) {
         # It's only safe to send one bytes unless you
         # somehow query the system to find otherwise.
         print($stdin_fh substr($stdin_buf, 0, 1, ''));
         # ...[ Do something if print returned an error. ]...
      }
     
      if (!length($stdin_buf)) {
         $writers->remove($fh);
      }
   }
}

waitpid($pid, 0);
# ...[ Do something if waitpid returned an error. ]...
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