I think that what is happening here is that the .mov files you are using contain a codec that is not compatible with iMovie. iMovie is more sensitive than QuickTimePlayer or the Finder to slight variations in formats. The .mov file format is particularly problematic because .mov is a bucket that contains a variety of codecs. .Mov files can differ from one another in the codecs that they contain. Not even all Mp4 files are compatible with iMovie. It must be Mp4/AAC, where AAC stands for Advanced Audio Coding. I suspect that the problem is with the audio codec.
So, what you need to do is to convert the .mov files, and even the Mp4 files that you "saved", by re-rendering them to Mp4/AAC. The files must be re-rendered, not just saved. Start with one of your .mov files and see what happens.
You can use the free download, Handbrake, to convert the files. Handbrake will convert them to Mp4/AAC by default. Doing that procedure often cures sound issues.
You can get Handbrake here:
https://handbrake.fr/
A simple way to do it is to open Handbrake and do a File/Open Source. Navigate to your video and choose it as the source from the resulting screen. (Click on Desktop in the sidebar to have the screen display the files on your desktop.) Then do File/Start Encoding. Wait a couple of minutes for the conversion to complete. Then save and import the converted clip into iMovie.
-- Rich