I think that your situation would benefit from a call to Apple Support. The techs there are very savvy and, further, have the capability of remote access to your computer. Click on the Contact Support item in the upper right hand corner of this forum's screen. Navigate to a phone number and give Support a call.
At first I suspected a corrupt library. But what is puzzling is that not only are your projects disappearing but also movies saved to your desktop won't open. Try opening iMovie while holding down the Option key only, and then selecting to create a new library in the box that appears.. Populate the new library with a project and see if it works properly and then see if you can share out the movie and open it on your desktop.
Also, possibly you have a hardware problem. Before calling Apple Support you could try running the Apple Diagnostics feature on your Mac (see Finder help menu) to see if a hardware problem is identified.
-- Rich