>This morning, I had suddently all icons on the desktop to be marked with a little X down the left corner. Now, most of the icons have this blue down arrow down the left corner. What is this a representation for?

When that happened, did you try clicking on one of the icons? I think that means that the application/file that it's pointing too is no longer found. Perhaps you had some type of backup running that was doing something weird with file-locking or something?