iMovie won't export and nothing I do will fix this. Help

Try deleting 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. Now see if the export feature is working.  Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.

-- Rich

Exporting to an ExFat external drive should work. But you can't put an iMovie library or Photos library on it, because to store and operate them requires a drive to be formatted APFS or Mac OS Extended (Journaled).

I would try formatting the external drive to APFS or to Mac OS Extended (Journaled). Then see if you can export to it. Be aware that reformatting a drive, if you go that route, will erase all data on the drive. So first backup all data that you want to keep.

-- Rich