(Update: added $species detection from @ARGV)

Here's the code...

my ($c, $species) = (0, shift());

while(<>) {
    chomp;
    next unless length;
    my ($seq, $scount) = split /\s+/;
    next if $scount < 2 || length $seq < 15 || length $seq > 30;
    print ">$species" . $c++ . "_count=$scount\n$seq\n";
}
[download]

If it's named process_sequences, then it could be invoked as:

process-sequences speciesname inputfilename >outputfilename

It's too bad the filenames aren't named for the species they represent, because then you could do something like this:

my ($c, $species) = (0, $ARGV[0]);

open my $outfh, '>', $species . ".new" || die $!;

while(<>) {
    chomp;
    if(length) {
        my ($seq, $scount) = split /\s+/;
        if($scount >= 2 && length $seq >= 15 && length $seq <= 30) {
            print $outfh ">$species" . $c++ . "_count=$scount\n$seq\n"
+;
        }
    }
    if (eof()) {
        ($species, $c) = ($ARGV[0], 0);
        close $outfh || die $!;
        open $outfh, '>', $species . ".new" || die $!;
    }
}
[download]

And that would be invoked with a list of filenames, each named for the species:

process-sequences bird bee cat dog