I know it's a big piece of code and looks ugly here. Sorry for this. If somebody has a hint for me - I would be very thankful :O)

It looks ugly anywhere :) seriously, subroutines should (for the most part) take arguments, not operate on global variables

You need more subroutines, there is way too much code outside of subroutines.

Instead of # build a list of files to check you need  my @resultfiles = files_to_check( $properties );

Your code contains exit 18 times -- way too many,

Your loop should be short, like

while( $client = $server->accept() ) {
    if( my $pid = fork() ){
        $logger->debug( "this is parent process closing client now" );
        $client->close();
        $logger->debug( "parent closed client" );
    } else {
        KidStuff( $client , $logger, $pid, ... );
    }
}
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This might interest you A suicidal parent OR death of a forking server

That's about all I got, except, you say you're using a browser -- then you might as well use write a plain old "CGI" PSGI, say with cgi-app / mojo / dancer / catalyst... and make it multithreaded with Perlbal or any other applicable server (feature of PSGI), instead of reinventing this particular wheel

Also, see Proc::Background :)