Can't move files from a iCloud or Desktop to external storage.

Seems like you might not have enough storage on the Mac to download the file. You probably need to free space. If your iCloud Drive folder exceeds the available space on your Mac, the Mac will try to keep as many files as possible locally. You may be better off storing your materials on an external drive in that case.

You may first need to move files already on your Mac (not in iCloud Drive) to free space. Or, use a different device to download some of your largest iCloud files and then delete those files to eventually free space on your Mac. Or, try to download the file in the iCloud Drive folder first (right click) the move that downloaded copy. Verify how much space you have in settings.

System data is managed by your computer. It is generally caches, Time Machine snapshots, etc. Some of the data may be cleared by restarting your Mac but most is simply managed by your device and freed is space becomes needed.

It appears that you are optimizing iCloud storage, so most files are not on your Mac but in iCloud only. Recommend downloading smaller files to your computer first (right-click on the file and select download). You can also try to drag/drop files to your home folder (or other location that does not sync on your hard drive). You can then move to an external drive.

If you have less stored in iCloud than the size of free space on your disk, you could also try turning off optimize. I'd guess something like 250GB in iCloud might still sync to your computer.

Or, you can download larger files by logging into iCloud.com. In Safari settings change your download location to either "ask for each download" or select "other" and point to your external drive. Once downloaded, you can delete the file from iCloud to save space.