The 4 is normally the System process ID. But something is causing it to do the work.
After moving that folder its still at 100% and just using different folders.
What is at 100%, the same folder after being moved is still being looked at or the drive itself?
When you look at Resource Monitor and set the CPU usage as priority, what is showing up as using the CPU. Keep in mind, a 0 does not always mean 0, it just does not show numbers less than that.
In resource Monitor, under Disk Activity, if it is really running 100% of the time, you must be showing some file that is showing a very large number of B/sec. Look through some of the other displays to see if anything shows up with a large amount of activity. If there are many files showing activity are they in the same folder?
Try watching the activity and see what changes when you take the disk offline...
Edit: I will add, if I check Resource Monitor for Disk Activity, every listed file in on the C: partition, and I do have other partitions and a second drive. If you are showing files on another drive, you should be able to pin them down. The system process has around 160 threads running in it. There is software that will break that out if you decide to try.