(1) I like to have a totally clean workspace/desktop and therefore put all the icons for the apps. I use on the top/bottom panels. In 11.4 I have done this for all the apps, I normally run except that the icons for TRASH and the HOME directory which cannot be deleted/moved to trash - the option is greyed out on the drop down menu. How does one get rid of these icons so as to have a totally clean workspace/desktop?
IIUC, you are looking for gnome3, right? sorry to break the news: There are no panels. I suggest you give the existing live images a try to see how much you like it.
As for gnome2, as you currently run and the question on how to remove TRASH and HOME, this should be possible in gconf-editor in the location: /apps/nautilus/desktop There are two booleans: home-icon_visible and trash_icon_visible. Switch them to FALSE (remove the tick) and the icons will disappear.
In GNOME 3, the icons will not show by default. In GNOME 2, playing with gconf is one way and another shortcut is: