Is it possible to store ALL documents in iCloud? If so, how shall I tell the system to do that?

Yes, and no.

The devil is in the details.

It's trivial to setup iCloud Drive to store all the files in your Documents folder.

System Preferences -> Apple ID -> iCloud Drive -> Options -> Desktop and Documents Folder

In this way, anything you save in your Documents folder are synched to the cloud - note that the key is synched - a local copy is maintained so that you can work on the document offline, and changes are asynchronously copied to iCloud.

However, this does not guarantee all files... if you save a document outside of the Documents folder then it won't be copied. Hence, as I said above, the devil is in the details.

If you're diligent about saving all your documents within your Documents folder, then you're all set, but there is no mechanism for making sure you do that - that one is on you.

See the article Set up iCloud Drive on all your devices - Apple Support

You cannot, not with iCloud. If you want offline storage — iCloud is primarily a synchronization service — you need to use some other provider.