Hi, skeneton,
It looks like the library that contained the projects either was deleted or that the link to it has been broken, or possibly you are opening iMovie in a different library than contains the projects. If the library is located on an external drive, possibly the drive has or is failing.
Close iMovie and look in your Movies folder (Finder Menu/Go/Home/Movies). See if there are other libraries in there and double click to open iMovie in them to see if they contain your projects. If you have an iMovie library located on an external drive, go there and open it.
If you keep a Time Machine backup you can restore your library to a point in time before the projects disappeared. Restore it to a different location so as not to overwrite your existing library.
To see if possibly a link has been broken, try deleting preferences. To delete preferences open iMovie while
holding down the Option and Command keys and select to delete preferences in the box that appears. iMovie will open in a new library. Reopen your old library to get back to your projects. Possibly you may need to reboot to set
the changes. Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.
-- Rich
