G'day tryingnottofailmytes,

Well, you do initialize them near the beginning of your script:

my $annotation = '';
my $dna = '';
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Their next appearance in your script is:

($annotation, $dna) = ($record =~ /^(LOCUS.*ORIGIN\s*\n)(.*)\/\/\n/s);
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where, presumably, you're setting both to undef (i.e. uninitialized).

When you then use them in the print statement on the following line:

print "$annotation, $dna\n";
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you get a warning about this.

For the other part of your question, see the use documentation.