Yes. You get rid of zombies on some systems, but you should rather use

use POSIX ":sys_wait_h";

$SIG{CHLD} = sub {
    my $kid;
    do {
        $kid = waitpid(-1,&WNOHANG);
    } until $kid == -1;
}
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No. This will not solve the problem of missing close. When open(FH,'...|') is called, pipe is created as a pair of file descriptors. These fil desrciptors will not be reused until explicitly closed by close syscall. Therefore if your program will serve thousands of requests in one process you will run out of file descriptors. One possible solution to this is to specify MaxRequestsPerChild 200 Apache configuration directive to limit one server process to serve only 200 requests before it dies. But the whole idea of long-running mod_perl precesses is somehow hindered by this.

All Zombie process are are child processes that have exited, but their parent hasn't called wait() yet to see what the child's return code was. They don't consume any resources except a process table entry.

When the child exits/dies, the parent gets sent SIGCHLD to notify it. If it doesn't call wait() in that signal handler, the child stays a zombie until wait() is called. If you haven't defined a signal handler, the default action will be to leave it as a zombie - after all, how does the OS know that you're not going to want that return code later?

Library calls like system() do the wait() for you. popen doesn't. That's what close FH is effectively doing on a popen'ed filehandle.