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If you've got linux with GNUstep installed, does a window manager come with GNUstep, or can you use any WM you like?
GNUstep is an API, a collection of libraries. You do not "run" GNUstep. So, yes, you will need _any_ window manager, but (currently) WindowMaker is preferred, as it best supports GNUstep.
I'd read that WindowMaker is written in C -- is there a WM that is written in obj-c and is specifically meant to go with GNUstep? Is an obj-c WM even desirable?
Correct, WindowMaker is written in C, and brings it's own NeXT'ish library, WINGs. Per se, WindowMaker has nothing to do with GNUstep, but is "tagged" as the window manager of choice.
And yes, there are window managers written in Objective-C, specifically for GNUstep, though work on them is in progress.
The most, uhm, advanced right now probably is InterfaceWM, at http://interfacewm.sourceforge.net/