Is it possible to make a Unity application like the Unity editor?

From many searches I've determined that the entire Unity editor/IDE is made similarly to how a GUI is made in a Unity application (lots of OnGUI's, confirmed by Aras). However, the Unity editor has a lot of functionality that is not in the Unity runtime (mainly, opening and closing of native windows). My goal is to make a specialized application similar to the Unity Editor, and a key feature of that would be to make native windows for Mac/Windows. Is this even possible? Is the Unity Editor just calling native APIs? If so, where can I get more information on calling native APIs from within the Unity runtime?

I don't think that creating a Unity application like the Unity editor would be possible. You already answered parts of your question: The Unity editor is a "native application". While it does use its own GUI-System for rendering most of the GUI (which made it easy for UT to make it cross-platform), it still has all the power of a native application.

Obviously, if you're using Unity Pro and are using native plugins, you could probably do almost anything ... but even then, I'm not sure it would be particularly convenient. In particular, I don't think you could use UnityGUI in any native Windows you'd create that way.

So, I guess the best you can do for now is write a feature request. As Unity is not only used for games but also for all kinds of non-game but 3d-interactive applications, opening "native Windows" might be a very useful feature. I guess even for some game UIs it might be useful (even though probably kind of unusual - but hey, enabling creativity also means allowing users to create unusual stuff ;-) ). As they already have parts of this functionality implemented for their own Editor, chances are that they could do it also for Unity games/applications.

See also Unity Feedback