Tabs that matched Conditions will be shown on the product page. It also depends on the other fields like Status, Website, Customer Group, From-To, Discard subsequent tab.
If the product tab is not showing on the frontend after add or edit, then do reindex by run the below CLI command php bin/magento indexer:reindex product_tabs_rule
Yes, to show the selected simple product's label set the Use for Parent to Yes under the Label Information tab. Reference guide: https://magediary.com/docs/product-labels.html#label-information