How did you download the songs? Did you download them from Apple Music or purchase them individually from the iTunes Store?
You cannot use the songs you saved from Apple Music in an iMovie Project, only purchased songs, that are not "Protected AAC". Occasionally older songs are only available at the iTunes Store as protected files, usually as a part of a collection album.
To see why the song cannot be used, open the song in the Music.app, open the Info with the key combination ⌘I and look at the "File" tab. What is shown as the "Kind" of the song? Does it show "Apple Music" or "Protected AAC audio file"?
If the song is neither Apple Music nor a protected AAC file, it may need downloading from iCloud, so it is a local copy.