Here is what happens when I import:
and here below is the message of error explaining the video cannot be imported because the "file would be damaged". However, all my videos are good and can be successfully imported if I would import then via iPhoto SW from Apple

please help...
This happens because the desktop version of Lightroom CC does not yet support HEVC video which is what your iPhone by default records in because it is much more efficient. If you import to CC through your phone in the Lightroom CC app on your phone (which is a more convenient method anyway than connecting your phone to your computer), I believe the phone will automatically transcode to H264 video which is supported in Lightroom CC and will show up on your desktop. Also the Photos app should transcode automatically. You can also set your phone to record H264 video by default in Settings>Camera>Formats. Move the setting to "Most compatible" and avoid the issue.