Grandfather's answered your first question already.

In answer to your second, you can use eval for this as well, but make sure you put apostrophes (') around the $1 in the assignment, rather than quotes ("), or you'll get an error.  Here's the code:

#!/usr/bin/perl

use strict;
use warnings;

my $string = "aaaaabbbbaaaaaa";
my $replace = '$1';
eval "\$string =~ s/a+(b+)a+/$replace/g";
print $string;
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bbbb
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Note that you need to use quotes (") around the eval statement so that $1 will interpolate, but (as Grandfather did) you still have to escape $string with the backslash "\" in the same line (\$string), so it won't interpolate.