2) When I use Nautilus in fluxbox, it creates a new window titled desktop that is just like my gnome desktop. I can't close it without explicitly killing it. Is there a way to keep it from creating the "Desktop" window while still using nautilus?
You can can call nautilus with the flag "nautilus -nodesktop" (or something similar). Doing so, the icons won't be displayed on the root window and only the file manager will pop up.
2b) If not, what is a nice graphical file manager besides konqueror and nautilus?
Nautilus is quite ok, but since you are using flux, you may want to stick with some other thing, non-gtk based stuff to speed up things. I use only MC (midnight commander), which is a command line file manager/editor. If you still want something graphical, go with emelfm (similar to MC), gentoo, etc. Here is a little list:
3) What is a command-line command I can use to bring up the fluxbox menu? It could either be specific to fluxbox or simply send a right-click event to the root window. Is this possible without writing custom software?
I don't think there's any. However, you can bind a key to access the RootMenu. Simply edit the file called "keys" on .fluxbox and bind a key to "RootMenu". Check those links if you are not sure how to do it: