Can I save page pictures from GreaseMonkey script directly to my hard drive?
Is the easiest way to do it - to setup my server and translate picture urls to it using GM_xmlhttpRequest ?
No, you can't. GreaseMonkey still is within the Browser sandbox and this means you cannot access any system resources. There is no FileSystem API in (browser-integrated) JavaScript anyway.
Maybe DownThemAll! helps you.