# Choose the Nth FASTA record
# Called as "perl script_name.pl line_number file_name"
use warnings;
use strict;

$/= '>';
my $line_number = shift;
while(<>)
   chomp;
   if ($.-1 == $line_number ) {
      print;
      exit 0;
   }
}
[download]

# Choose any Range of FASTA records
# Called as perl script_name.pl --start start_line --end end_line file
+_name
# both --start and --end are optional;
# no --start => start reading from end of file, end at --end
# no --end => start reading from --start, read to end of file
# neither => print every line
use warnings;
use strict;

use Getopt::Long;
my ($start, $end) = (undef, undef);
GetOptions(
   "start=i" => \$start,
   "end=i" => \$end,
);
$/='>';
while(<>) {
   if(
     (!defined($start) || $start <= $.) &&
     (!defined($end) || $. <= $end)
   ) {
      print;
}
[download]

As for your "show the number of lines" example, I don't understand it. From the looks of it, it looks like it counts the number of lines in the file that have a whitespace character in it. Is this really what you want?