Is there a way to start coping all the files from a external hard-drive to another external hard-drive automatically when it's inserted?
I don't know the drive letter of both drives before. Is this possible without me being there?
I think I've once used Allway Sync for exactly that purpose. It offers one-way sync and bidirectional sync for external drives.
This sync process can be triggered automatically when a drive is inserted. I guess you'd have to plug in the receiving drive first and then the source drive.
The tool is free, but with a (very generous) limited amount of files per month. Just try and see if it fits your needs!