Is it at all possible to make the content in a DIV appear in the same exact position on screen no matter how much you scroll? If so, how? Or, not quite as importantly, is it possible to make it stay in the same place only horizontally? It is important that I get at least the first and possibly the second.

depends, i don't think there is a way to make it stay in the same place whichever way you scroll. however, if you position the div to botton and right, it won't move as much because normally the window is resized from the top and left.

perhaps like this?
http://www.dynamicdrive.com/dynamicindex4/logo.htm

Sorta like that, but not in a corner