no. they have to download the images to view them. the web server can't tell the difference between a browser downloading to cache to be viewed on the web page or downloading to the desktop to be saved for later.
see above. web logs have a record of all users downloading all pages/images, but can't tell you where the image is going (desktop or part of the web page)
only real way to do what you want would be with an application that restricts what the user can do, not with a web page.