I would like to hand edit a Visual Studio team settings file to make a few changes. Is there a documented schema anywhere (either XSD or English prose) for .vssettings files?
Could you please elaborate on what you want to edit, and why? I'd be very surprised if you came across something that isn't settable from the GUI. If you need to automate some IDE setup across multiple machines, I'd suggest IDE macros.
Technically - the answer is no. vssettings files are not validated against any schema, documented or not.
In case it isn't obvious from the element names how to achieve what you want - you might, for example, set the desired option with the GUI and diff the resulting vssettings with the initial one.
But, again, why would you want to do that?