#!/usr/bin/perl
use strict;
use warnings;
use feature 'say';

my $last = '';                                    # Remember the id.
my $count_1_x;
my $count_nonblank;
while (<DATA>) {
    my ($id, $col2, $col3) = split;
    if ($id ne $last) {                           # A new record begin
+s.
        say "$last $count_1_x $count_nonblank"
            if $last;                             # Do not print at th
+e very beginning.
        $last = $id;
        $count_1_x = $count_nonblank = 0;
    }
    $count_1_x++      if '1_x' eq $col2;
    $count_nonblank++ if defined $col3 and length $col3;
}
say "$last $count_1_x $count_nonblank" if $last;  # Print for the last
+ record.

__DATA__
A 1_x 9_z
A 1_x 
A 1_x g_z
B 2_c 
B 1_x 1_z
C 1_x 1_z
C v_x 8_z 
D v_x s_x
E 1_x 
F
[download]

This was more an experiment in whether it would be possible, than a piece of sound advice...

use 5.010;
use List::MoreUtils qw< part >;

say for
    map {
        my $x = $_;
        sprintf(
            '%s %d,%d',
            $x->[0][0],
            scalar(grep { $_->[1] eq '1_x' } @$x),
            scalar(grep { defined $_->[2] } @$x), 
        )
    }
    part {
        # me thinks List::MoreUtils needs a way to make this simpler
        state $part = 0;
        state $last = undef;
        $part++ if defined $last && $last ne $_->[0];
        $last = $_->[0];
        $part
    }
    map { chomp; [split /\s+/] }
    sort <DATA>;

__DATA__
A 1_x 9_z
A 1_x 
A 1_x g_z
B 2_c 
B 1_x 1_z
C 1_x 1_z
C v_x 8_z
[download]

perl -E'sub Monkey::do{say$_,for@_,do{($monkey=[caller(0)]->[3])=~s{::}{ }and$monkey}}"Monkey say"->Monkey::do'

use 5.010;

my %parsed;
while ( <DATA> ){
   my @tmp = split;
   $parsed{$tmp[0]}{x1}++ if $tmp[1] eq '1_x';
   $parsed{$tmp[0]}{c3}++ if @tmp > 2;
}

for my $k ( sort keys %parsed ) {
  say join ' ', $k, $parsed{$k}->{x1}, $parsed{$k}->{c3};
}

__DATA__
A 1_x 9_z
A 1_x 
A 1_x g_z
B 2_c 
B 1_x 1_z
C 1_x 1_z
C v_x 8_z
[download]

Update: The output part of the above code breaks for a given ID if (a) '1_x' never appears in column 2, or (b) '1_x' appears in column 2 but there is never a third column for this ID. To understand what I mean, add the following lines to __DATA__:

D v_x s_x
E 1_x
[download]

Solution: change the line in the for loop to:

I saw Not_a_Number's solution as I was about to post mine. I've added his extra test data plus an additional one of my own which has nothing in either column 2 or 3.

#!/usr/bin/env perl

use 5.010;
use strict;
use warnings;

my %result;

while (<DATA>) {
    map {
        $result{$_->[0]}[0] += defined $_->[1] && $_->[1] eq q{1_x} ? 
+1 : 0;
        $result{$_->[0]}[1] += defined $_->[2] ? 1 : 0;
    } ([split]);
}

say qq{$_ }, join q{,} => @{$result{$_}} for sort keys %result;

__DATA__
A 1_x 9_z
A 1_x 
A 1_x g_z
B 2_c 
B 1_x 1_z
C 1_x 1_z
C v_x 8_z 
D v_x s_x
E 1_x
F
[download]

This outputs:

$ pm_extract_1_x.pl
A 3,2
B 1,1
C 1,2
D 0,1
E 1,0
F 0,0
[download]

OP here. That looks brilliant thanks very much for that.