I am a little confused as to what procedure you are following to move your iMovie "stuff" to an external drive, and what in general you are trying to do. Is the "stuff" you are moving your iMovie Library or is it separate iMovie Projects, or is it finalized movies? When you say "test movies" are you referring to test projects? Are you deleting projects from your iMovie app?
If you can explain further what you are trying to do and what procedures that you followed, we could better address your issues.
The way to move your iMovie Library to an external drive is first to format your external drive to Mac OS Extended (Journaled) and then copy your iMovie Library (select its icon in the Movies folder, and do an Edit/Copy) and then Edit/Paste it into the external drive. If the copied library works fine on your external drive, you can delete the one on your Mac. Or you can drag your iMovie Library to your external drive, which is less safe because accidents can happen while dragging. NOTE: Reformatting a drive erases all data on it, so before reformatting backup any data on the external drive that you want to keep.
Likewise if you are moving your Photos Library, as opposed to individual photos, the Photos Library needs to be stored on a drive that is formatted Mac OS Extended (Journaled). I can't tell whether you are trying to move your Photos library to an external drive or trying to move individual photos there.
As for the "My Movie" item in the iMovie sidebar in your screen shot, that is an event, not a project. It contains the media that is used in the project by the same name. If you have deleted a project from the iMovie app, the event will still remain, as well as the media in it, unless you delete the entire event itself (not just the media in it). That will remove all media from the iMovie library and, of course, that media will be deleted from all remaining projects that might be using it.
Next, you cannot open a project from the Finder via the Show Package Contents of the iMovie Library. The package contents contain only data and codes that the iMovie app assembles into a project when you open a project from within the iMovie app. You must not move, modify, rename or change in any way the items that you see in the Show Package Contents, or you risk corrupting your iMovie library.
I suggest that you look through the following help link, that has a good search feature, to familiarize yourself with the procedures for moving libraries and files:
https://help.apple.com/imovie/mac/10.1/
-- Rich