k one is a disk image compacted (the dmg), the other is the mounted disk image with the installer inside. Ignore both of those for now. On the menu bar, use the Go menu & choose Applications & find LimeWire folder. Open that folder, the LW program will be inside. Drag & drop it into the dock. Remove the other LW files from desktop. Make a back up of the dmg. Now when you wish to open LW you simply click on the LW icon in the dock.

BTW sorry for the very late reply.

LimeWire does not show up in Applications, or anywhere else. Only the icon on the desktop. This happened each time I tried to install it - it never shows up anywhere else except on the desktop. How can I get it to show up in Applications so I can make it work?