2/ “….which is the logical way to display” – we recommend that you contact the support team of the WooCommerce plugin – https://wordpress.org/support/plugin/woocommerce/ , because there are no additional settings for this from our theme side, unfortunately.
3/ “Hide out of stock items from the catalog” needs to be enabled in WooCommerce > Settings > Products > Inventory.
If you have any additional questions or concerns, please do not hesitate to reach out to us. Our support team is always available to assist you.
