You can install the desktop on the RetroPie image and other packages (including a browser) so you can operate directly from the Pi. See here.

Does the RAW backup then also occupy as much space as there is data on the SD card or is it then a 1:1 image of the entire SD card and its capacity?

If you look in the topic for the utility I pointed, there's an explanation on how much space does it take - it will initially create a full block copy of your sdcard, then shrink it to the actual size of used blocks. So you need to have enough space on your USB disc for a full sdcard copy.