From your description, it sounds like you are prompted to "link missing files" when attempting to modify/move certain items. iTunes has lost track of the actual song file that is on your computer, and we'll need to instruct iTunes on where this file is located. The following information will assist you in tracking down these missing files:
If you can't find your media, you may be able to download it again if you originally purchased it from the iTunes Store:
This is a visual cue that iTunes will link to the files in their current locations. Contrast with the behavior when the files you are adding are located outside the media folder and the option to Copy files to the media folder when adding to the library is enabled. In the latter case iTunes will make new copies of each file, add them to the library, and add them to the playlist.