Hi,
We checked your site and this are some points we noted different from normal woocommerce behaviour
1) address are not been saved in the session, when you are filling the address detail in our calculator and you refresh the details are gone (this should not happen as those details get saved in the Woocommerce address session)
this address are not even saved when you fill them out in the Woocommerce checkout page, you fill the address in checkout page and once you refresh all the details are gone, generally WooCommerce retains the address
=> this is happening due to some plugin
2) your shipping method is based on the City because when we selected only State: Atacama it did not show the shipping method on checkout page , when we selected the city then it showed the shipping method name
but in the calculator you have hidden the city column
you need to enable the city column as your shipping method is based on city