3/ The description is only being visible if a product is added in that category, or else it’s not being visible. -> Yes it is hidden if there are no products added for this category and instead of that we show ‘No results found’ text there.
If you need to add custom description/text/html for specific category you can add it via -> https://gyazo.com/fab9a873ad123d32ef2ec5dbc1dd8b5e (description and description after content fields).
Please note that additional customization is not included in basic theme support. You can submit customization request here, or copy from parent and rewrite via child-theme/woocommerce/archive-product.php
