Hi,
To finalize the movie click on the Share option shown in the File menu drop down in your posted screen shot. Share the movie to your desktop, choosing the quality setting of "High", not "Best Quality (pro res)".
iMovie can export in 1080p up to 60 fps, and 4K 30fps. Perhaps if your GoPro video is in a different resolution, that might be causing the issue.
Everything exported out of iMovie is Mp4/AAC, except when exported at the "Best" quality setting, in which case you will get a .mov file that is about 4x larger that the Mp4 file, as you have found. Exporting in "Best" quality is not advisable for normal consumer usage.
Sometimes iMovie preferences can go awry, and that can cause iMovie to function improperly. Try deleting/resetting preferences. To delete, reset 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 empty library. Reopen your old library to get back to your projects. Now see if iMovie functions properly. 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