Hi,
The songs are not usable in iMovie because they are DRM (Digital Rights Management) protected. From what I have read Apple Music contains DRM protection. Music sold on iTunes prior to 2009 also is DRM protected. iTunes has a program called "Match" that you can subscribe to for about $25 that will let you download from the cloud DRM free duplicates of your protected songs, provided that iTunes still sells the song.
You said that you used these songs in iMovie a year ago. Therefore they probably are still in your iMovie library and you are free to use them again if you want. You might be able to go back to your old projects and pull those songs out for use in a new project. Assuming you are using iMovie 10, go to an old project where the song was working, select the song in the timeline, do a File/Reveal in Finder. A folder will pop up called Original Media and it will have the song highlighted. Option-drag (i.e, copy, not move) the song to your desktop. You should be able to drag the song from your desktop into a new iMovie project.
Another way would be to select the song from the old project, and copy-paste it into your current project. Or paste it into a newly created project and share out that project as an Audio Only file. That would give you an audio file that you should be able to drag into a new project.
Another way would be to make a duplicate of the old project, open the duplicate, and delete everything out of it except the song you want. Then use the depleted duplicate to make your new project.
-- Rich
