A. A. It is not possible to delete the icon, however you can make it invisible.
- Right click on the desktop and select Properties
- Select the Plus tab
- Select "My Computer" and click "Change Icon"
- Change the file name to "%systemroot%\system32\tweakui.cpl"
- Select the 4th icon (a big blank) and click OK
- 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.