Can I retrieve all additional addresses

Take a look at the My Account template and you can see how this is rendered. https://github.com/crosspeaksoftware/woo-address-book/blob/748f78aa700f8d98238c7d803607a2731fec5879/templates/myaccount/my-address-book.php

Basically you can use the following code to get an array of addresses in the address book and then loop through them as outlined in the template.

$wc_address_book = WC_Address_Book::get_instance();

$billing_address_book  = $wc_address_book->get_address_book( get_current_user_id(), 'billing' );
$shipping_address_book = $wc_address_book->get_address_book( get_current_user_id(), 'shipping' );