I used the migration assistant from my old to new Mac, but both my macs are connected to the icloud... in this case, does "turning off" the icloud from the old computer allow me to delete said documents without damage?
The intent of iCloud is to make the connected things exactly the same on all connected devices. If you disconnect a device from iCloud, then changes won't be copied to iCloud or anything else. But-- if you reconnect, then those things will be copied from iCloud back to the device.
You can choose what's synched to iCloud at System Settings[name]>iCloud:
So you can turn off just messages, say, and delete them without bothering anything else.
If you turn off iCloud Drive, then you can have the files in it kept in the local iCloud Drive Folder, but that's renamed "iCloud Drive (Archive)" and shows up in your own User's account.
Deleting iCloud docs after Mac migration
