Unpublished categories are still searchable and can't delete categories

I have found that when I unpublish a category in the backend, the posts within that category are still searchable. That seems wrong!

I have also found that I can't delete a category in the backend. I check the box next to the category name, scroll to the top, click delete, and when the page refreshes the category is still there. No error message or success message. Bug!