All downloaded or downloading files will go to the library. Incomplete files found in incomplete folder. Downloaded files found in Saved Files folder. As for Shared folder, check your settings. Only files shared will go into there & be visible AFAIK. LW's menu bar, Tools>Options>Sharing & at bottom of window is Download Sharing. Check this option if you want all downloads shared & shown in the Shared folder. If you don't have this option ticked, then it may take a while before they show up in the Shared folder.

Another small complication is if you right click a download & choose a different download location. However, with the above option ticked it should still show in the library.