If I power off my computer will my imovie projects automatically save?

I'm not familiar with iMovie, but generally if you try to shut down your Mac and any applications or documents are open, it will ask you if you want to save the files and also warn you if you really want to shut down because there are open files.

If you are using iMovie 11 or iMovie 09 or iMovie 08, your Project saves automatically as you go. It does not wait until you shut down. So if you shut down, yes, your projects are saved, but the saving happens before then.

In iMovie, your actual video clips are in Events. Usually they are in an iMovie Event, but they could also be in an iPhoto Event.

When you edit a Project, you are creating a text document in hexadecimal format that contains a list of instructions that are executed to create your movie. When you see your project in the viewer, you are really seeing these instructions being executed in real time. The instructions provide the path and the in and out points for the clips used in the project, and also paths for any photos used, text and type of titles, transitions, color correction, paths to audio, etc. Because it is recording instructions and not actually rendering a movie, the editing is very fast, and you can undo the last few actions. It also means that saves happen automatically and they are very quick.

When you use the Share menu to create a final movie, the movie is created by executing all the instructions in the Project, and now you have a movie that you can play and share/