Hello,
1- Sorry to say but as you know the Cart page comes from WooCommerce by default, so the elements are not editable there directly with the page builder plugins. You can check the Dashboard > WooCommerce > Settings > for the available options in this regard.
2- Regarding the Shipping method not working concern, could you please once try deactivating all the third party Plugins on your Site, remaining the Theme required ones activated. If the issue gets resolved, then reactivate them one by one to see which Plugin is causing the issue.
If somehow the issue still persists, then please take complete Backup of your Site first, then provide us the WP-ADMIN Login details of your Site in the Private Content field along with the permission to completely debug your Site which includes deactivating all the third party Plugins and removal of on-Site Customization changes too, so that we can thoroughly check this issue on your Site and assist you accordingly.
Best Regards.