Hello,
1. The option in the settings is called “stock status” and not “out of stock status”, so it works correctly, and we will add an additional option only if it is often requested by our customers as a feature request.
2. Its problem cannot be solved with hooks, but it is most likely possible to solve it with CSS. In order to prepare such a custom, we first need to see how his site is configured, so we need a link to the product page. Please share the product page and we will try to give the custom CSS code.
Best Regards.