So, the ones you are showing on the Desktop (in the image) are not really there? That (I guess) answers my first question. Any chance on answering the rest of them? I'll go back and number them...
An additional question:
Do you have any idea how the icons shown in the image got back onto the Desktop or why they, perhaps, did
not disappear? [note: there are two questions in that sentence]
Just an idea, but if, while the Desktop is the active window, you happen to press command-A, you will select everything on the Desktop. A simple, but fast drag to any edge will take the majority of the icons outside the visible part of the window.
BTW, thanks for making a reasonably sized image to post.