Files that completely download are moved to the folder/directory you set for "saved"--incomplete files are stored in the "incomplete" folder. Only folders that you share (and the incomplete folder which is not shared) show up in the Library Pane, so if you have chosen not to share your download folder, it won't show up in the Library Pane.

Look at you harddrive and your preferences to see what is stored and where.

Not all files you try to download succeed.