A Space just for an App Is there a way (perhaps using a third-party app) to make one of my Spaces permanently locked to a single app (in this case, TextEdit)?

I want to have all my TextEdit windows and nothing else in one Space, at all times.  I never want TextEdit to open windows anywhere besides my TextEdit-dedicated Space.
In 10.7 and up, you can assign apps to Desktops. To assign an app, Control+click the app's Dock icon, navigate to Options and then choose to assign it either to All Desktops, This Desktop or None. 

All Desktops assigns the app to be open on whatever Desktop you switch to. If you have it open on Desktop 1, and switch to Desktop 2, it will appear to not have moved. 

This Desktop assigns the app to a specific Desktop, and force it to always open there. This is the option I would try to accomplish your goal. 

None is the default setting, and leaves the app unbound by any Desktop-specific rules.