i want to copy whole lists/libraries from the root-site to subsites with the actual content/items in it.
What is the best way to realize this?
Use Nintex workflow - Call web service sharepoint to get all your lists and librairies.
After that you can make a loop on each lists and librairies and use again Nintex workflow - Call web service on Web URL/_vti_bin/Copy.asmx
Usually I use the web method CopyIntoitemsLocal with the sourceUrl and the DesunationUrl (automatically all metadata are copied)
I would seriously recommend using PowerShell if you can for this. The above comments are good instructions and can be done, but you can do a simple site backup and restore that site to whatever url is defined. You could then run the PowerShell script from a workflow if needed for scheduling purposes.