Can a desktop monitor operate using the laptop`s operating system via the VGA cable?

Yes, using a simple RGB or VGA cable, it is possible to do that stuff.

Yes it is possible, all the laptops having VGA port it is the same only comparing with Desktop VGA.

if want to see your leptop desktop data, open your leptop from bottam get sata harddrive outside use this harddisk in your desktop instead of desktop hardisk and boot disk with leptop HDD it will work if win7 is in leptop’s hdd and if xp then am not sure that u ca boot

for win xp secont mathed is add leptops harddisk in desktop open C: or D: drive of leptop hdd and go this add- C:/Documents and Settings/Administrator/Desktop or C:/Documents and Settings/All Users/Desktop