I can't reproduce it on a clean FC 17 KDE spin image I installed this morning.
To be clear, (1) from your original message is correct. Slickedit is not adding itself to the application menu automatically.
For (2) I get the icon if I manually add the app. Also, if I browse over to the slickedit install directory, and start it from the file manager, the icon in the task manager looks good, and an entry for slickedit shows up in the desktop folder view, with the icon in place.
For (3) I'm seeing the icon in both the standard task manager in the bottom panel, and in the icon-only manager widget I dragged onto the desktop.
Out of curiosity, what do you see if you go the the bin directory of the slickedit install, and double click on vs.xpm? Should just be the slickedit icon in whatever your default image viewer is.