A. A. It is not possible to delete the icon, however you can make it invisible.

  1. Right click on the desktop and select Properties
  2. Select the Plus tab
  3. Select "My Computer" and click "Change Icon"
  4. Change the file name to "%systemroot%\system32\tweakui.cpl"
  5. Select the 4th icon (a big blank) and click OK
  6. Click Apply then click OK

You could then move the icon to the bottom of the screen to hide the "My Computer" text.

Now, don't use autoarrange, and don't select a greater screen resolution and you will never see it again.