I installed the facebook application but there is no icon on the home screen application list. How do it get it there?

Look in your Applications folder. It's probably there.
If not, then it might be hidden. Just unhide it using the 'Show All' option from the home screen menu.

it's listed in the applications list under "Advanced Options" but the icon won't show up on the main screen, even when "show all" is checked.

Do you have an Applications folder? It should be an icon on your home screen called 'Applications'.
It's probably in there.

I seem to be missing the icon for it as well. It is installed, and I can run it from the blackberry app world, but i don't appear to have an icon for it in my apps or downloads folder.

You probably have a Beta of OS 5 installed then. Since the app isn't compatible with OS 5, it's the first thing that comes to mind.