I believe that is an Apple II ProDOS Floppy image.
Here is a floppy writer (that hopefully works ) for this image type: http://www.lazilong.com/apple_II/adfs/
If it doesn't work, your dsk images(get it?) might be corrupted.

.dsk? Its mini vMac disc image?
Run it under mini vMac. Use Disk Copy to make .img image

The USB Floppy might be a problem as they often only write to 1.4 MB Floppies. They read 800KB but seems to get lost when trying to write. My experiences comes from using FlashBuster (Y-E Data) whith these specs for format:

Compatible media and format

• 2HD Mac standerd 1.4 MB: Read / Write
• 2HD DOS 1.44 MB: Read / Write
• 2DD DOS 720 KB: Read / Write

I've checked Disk Copy 6.3

Feed Disk Copy 6.3 with these images by its Apple-K key combination ("Convert image" menu command).
Save as "read/write" or Disk Copy 4.2, the latter mainly if the game enclosed is a vMac game.

As for installing out of disk image files, this is like installing from real floppies if no copy protection come across. If you manage to mount the .dsk files or its converted Disk Copy .img counterparts, you can surely install your software out of the images, even on real hardware.

Some downloads of this site are available as .dsk.zip files. Usually the emulators and probably the real hardware should handle them like any other disk.

From using other emus and utilities I remember .DSK standing for a raw dump, as you mention; ´til the last byte, with nothing else. Like a .CDR under OSX. Do you have an example of these .DSKs online somewhere?

Do you have an example of these .DSKs online somewhere? "

Mystery Master: Murder by the Dozen

The .dsk files seem to be supported by Mini vMac, yes, but I don't want to use it on an emulator but on the real hardware! As far as I understand, it is an image of the complete disk, 'till the last byte. Now I'm sure there must be a way to use these images to create "real life" floppy disks to work on my LC III?

You could try (on copies of) these .dsk image files, changing the Creator and File Types to:

"Creator Type": ddsk
and
"File Type": dimg

This makes a Read/Write "Disk Copy 6.x" file that you can double-click to mount and/or do other other disk image tasks, as you can do with Disk Copy 6.

I've had a lot of success using this method on image files from .dsk .ima .hfv to .iso - floppy disk size images to CD size and also image files up to 2 GB in size on Mac OS 7.x to 9.2.2

I use the Q&D program "Creator Changer" to make the Type changes, but you can use other similar programs and also ResEdit to do the same. Creator Changer is here if you want to try it:
http://www.macintoshgarden.org/apps/creator-changer-284-0

It may or may not work on your particular .dsk image files, but its worth a shot. Good Luck.

Mystery Master: Murder by the Dozen

This appears to be a DiskDup+ image file, which the OP says could not access his particular .dsk files, which may or may not be DiskDup+ files.

However the Murder by the Dozen.dsk file can be opened in Disk Copy 6.x if the Creator and File types of the .dsk file are changed to ddsk and dimg respectively.

Caveat, it requires a Mac OS less than version 8.0 here, because this partictular image file is MSF formatted, which is not supported in 8.0 or later.

I was able to after changing the Creator and File types, open this in Disk Copy 6.x on Mac OS 7.6.1 (Basilisk). To make use of this image on a real Mac running 9.x the image would need to be further converted to a non MFS format - converting and saving the image as a 1.4MB floppy works (and would also be able to be written to an external USB floppy on newer Macs such as the OPs).

HTH