Your problem is that each fasta sequence spans multiple lines. Knowing that the fasta header is ">" you can use that to your advantage by telling your program to split around the fasta separator and slurp all that is in between. Another neater solution is achievable through Bio::SeqIO which requires BioPerl installation on your system. So for the first case, slurping each fasta record the following code gets you there with few modifications, improtantly, note the default separator variable $/was locally modified to ">"

use strict;
use warnings;
use Data::Dumper;

local $/=">";
while(my $fasta_record=<DATA>){
    chomp $fasta_record;
    $fasta_record =~ s/(^>*.+\n)/$1: /;  #add a space after the fasta 
+header 
    $fasta_record =~ s/\n//g;  # remove endlines
    print $fasta_record,"\n";
    }

__DATA__
>protein1
WWWWTCTG
TTWTTTCT
TTWWWC
>protein2
WWWWTCTG
TTWWWC
TTWTTTCT
>protein3
TTWWWC
WWWWTCTG
TTWTTTCT
[download]

I prefer using a BioPerl module to do this kind of tasks since I can get more time to focus on the more important stuff of doing something or the other with the sequences rather than grapple with how to read them in

Assuming that your sequences are in a fasta file called database_filename.fa

use strict;
use warnings;
use Bio::SeqIO;

#initialize a bioperl object instance
my $in = Bio::SeqIO->new(-file=> "database_filename.fa", -format=>"fas
+ta"); 
while(my $seq = $in->next_seq){    #read the sequences in the bioperl 
+object
    print $seq->id," ",$seq->seq; #output,ID space-separated from sequ
+ences 
    print "\n";
    }
[download]

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