You're getting closer with the second, but && is the boolean AND operator (& is the bitwise AND; see perlop for more details).
And using grep might be a bit more idiomatic, especially since the numbered variable names is a common red flag that you should really be using an array instead.
my @statuses = _frobulate_status_processes( );
my $running_frobulators = grep { m/\A Running \z/xi } @statuses;
if( @statuses == $running_frobulators ) {
print "All processes frobulating\n";
} else {
print "Only $running_frobulators of ", scalar @statuses, " running\n
+";
}