AFTER you solve the problem with the library, by the way, this is what you wanted to do:
1a) When you mention the "shortcuts" at the "bottom" (the dock), are you talking about a folder? If you use iPhoto a lot, you can have it (or any application) always show in the dock, and not within a folder. When app. is running and showing in dock, hold down on the icon until you see some choices, and choose "keep in dock."
1b) If you really want the application to be on the desktop: in finder, go to applications and choose iPhoto.app. Click CMD-L (or, File-make alias) That will make an alias "shortcut" to the application. Move the alias to the desktop.
2a) If you want to make a back-up copy of your photos, the best way is to do it within iPhoto: file-export. You can do it by album, or all photos.
2b) If you want to make a backup of your entire iPhoto library, which saves albums, etc., you should copy the entire library onto an external drive (so you don't have the problem of finding the correct library, or 2 different libraries)