There are two ways to achieve your goal:
- in the quiz change all the image URLs to absolute URLs. They can even refer back to the kind lady's server. Then the quiz could run on your Moodle site without any changes or need to move the images
- move the images into the same folder as the quiz (or a subfolder of the folder where the quiz resides) and then use relative URLs for the images
As for unzipping, are you aware that Moodle offers you an "unzip" link for zip files that are listed in the "Files" area for a course? It is not such a painful experience
hope that helps
Gordon