1. When the screen-saver is activated, does the scanner take up where it left off the last time or does it start all over again?

if i’m not wrong…it will start all over again…

2. I have the power settings set to turn the monitor off after 15 minutes and the hard disks off after 20 minutes of idle time. Will the scanner still operate after these settings take effect?

i’m not too sure about this…perhaps it worth some trial & error

Maybe I should set them so that they will not kick in until after the time it takes for a full scan (in my case - about 20 minutes.)?

not a bad idea

3. With 'Loop scanning' unchecked in the screen-saver settings, does the scanner stop after it has done one complete scan?

yes…if the screensaver remains uninterrupted