I think this will work for your first question:

my $shortname = $bfile;
$shortname =~ s!.*[\\/]!!;
my $member = $zip->addFile($bfile, $shortname);
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As to your second question, I think (untested) you can read the file and just ignore the contents, but check to make sure you don't get errors:

my $ziptest = Archive::Zip->new($bfiledst);
if (!defined($ziptest)) {
  # big error;
}
my @members = $ziptest->members;
#check to make sure it has what you expect

#then check individual files:

for (@members) {
  if (! defined($ziptest->contents($_))
    # another error.
  }
}
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Of course you should test that with some corrupted zip files to make sure it works.