Hard drive transfer to external hard drive

The disk drive shown in your screenshot - INTENSO - should be reformatted for proper use with macOS. It is currently using the MS-DOS FAT-32 format.

You need click the Erase button in the toolbar, then use Mac OS Extended (Journaled) as the format and GUID as the partition scheme.

Afterward you should be able to use it as you like with your Mac.

Any data currently stored on that drive will be erased when you partition it.

You need to use the folder icons in the sidebar to locate and open the folder where your documents are, then drag those documents onto the Intenso disk drive icon that you also see in the sidebar.

• Double-click to open the folder where the files are located on your internal drive. Usually in the "Documents" folder.

• To select multiple files and folders, click on the first one to select it, then press the option key when you select a second, third, forth file, etc.

• Click-and-drag your files and folders from that location on your internal drive over to the external drive that you see in the left sidebar.

Also, please see these:

Organize files in folders on Mac - Apple Support

Use external storage devices with Mac - Apple Support

Great catch! :)

Format or Erase the drive to MacOS Extended Journaled or ExFAT if needed for Windows & Mac. APFS if there us no other choice.

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Your original post is quite vague, but it occurs to me that maybe your Mac is stuck in recovery mode or some other odd limbo.

I see that you can use Disk Utility and Finder apparently without issue.

Have you attempted to restart the Mac?

You can force a restart by pressing and holding the power button until the Mac shuts down. Then press it again to restart.

You say your Mac has been "like this for a week". I'm not sure what that means. It might be helpful if you can provide additional details as to how you came to be in this spot. Zombie mode?