They are for companies Opera contracts with, and appear when Opera is updated. If you delete them, they should stay gone, but there will still be new ones from time to time.
I have also deleted my Speed Dials when the delete button suddenly appeared where I intended to select.
Why do buttons like this even need to be hidden part of the time?
I guess this is supposed to be a cleaner look, but it takes away from the useability when I have to go hunting for controls that are sometimes hidden.
I have the same problems with some of the controls in the new bookmarks manager and some of the settings.
Not that I'm aware of. i urge it here in this add-on forum as a useful keyboard-shortcut feature for for an Opera add-on.
You might want to post a request for this type of keyboard functionality also in the Suggestion forum for an Opera feature. You could mention that all the other browsers provide that shortcut as part of the native browser, and it is useful.