You can associate different artwork with each song - just right click on the song, select the Artwork tab and use any of the standard methods - Add Artwork button, drag-and-drop image file from Windows Explorer, copy to clipboard and then paste (Ctrl-V or right-click paste works in iTunes 11, Ctrl-V only in iTunes 12). However, when you view the album in iTunes it will only display one image (I think that it is automatically the image for disc 1/track 1, or the first track that has an associated image). When you play the album in iTunes or on an iPod, the image should change to the one for each individual track.
There is, though, no concept of an "album cover", i.e., an image that's associated with the album rather than its constituent tracks. If you try and associate an image with the album (right-click > Get Info > Artwork) this will replace the images associated with individual tracks. It is possible to have more than one image associated with a song, though this is not really a useful function since there is no capability in iTunes to display the alternate images except in the Get Info editor.
For the other issue, iTunes will always automatically display "Various Artists" for the album when:
- tracks have different Artist values,
- the Album Artist value is blank for all tracks, and
- the "Part of a Compilation" flag is set for all tracks.
You can also manage compilation albums by setting the Album Artist to a common value for all tracks (this can be anything you want) and unsetting the "Part of a Compilation" flag. The latter is really necessary only with older iPod models that don't recognize the Album Artist tag. The other effects of doing this way are that:
- compilations will be sorted based on the value you set for Album Artist (or, if desired, Sort Album Artist) - if you use the method based on the "Part of a Compilation" flag compilations will always be listed at the end of your library, assuming sorting by Artist.
- if you've configured iTunes to organize your library, compilations will be stored in iTunes Media\Music\album_artist\album_title - if you use the method based on the "Part of a Compilation" flag they will be stored in iTunes Media\Music\Compilations\album_title