If it doesn’t appear on the top right your topic contains only a post (or a few short posts). That’s why you can find another wrench icon even at the end of the topic
Yes, even if it is not mandatory to use the categories, you can use the Uncategorized “category” (if you have not disabled it from site settings) - which is not a real category - as is done for the Welcome topic that you find in every Discourse installation.
Anons and normal users can see (and dismiss) the banner. If you want to display it ONLY to anon you need to add a few lines of CSS to your main theme(s)