They are documented, right there in the code, note the XML documentation comments (the lines starting with
Now true, the documentation can still be improved quite a bit, but I think most of them are reasonably clear, like:
/// True if the request is for localhost domain
public static bool IsDeveloperMode
So if you are running a debug session from Visual Studio, your development server is typically http://localhost:31544/, and the property
IsDeveloperMode will be true on any requests coming from a
/// The current request localization
public static Localization Localization
Localization is a bit more complex, it however points to a class, (which if you have all the source code in Visual Studio, should be easy to find). Take a look at https://github.com/sdl/dxa-web-application-dotnet/blob/master/Sdl.Web.Common/Configuration/Localization.cs
This basically is a container for the Publication information the request is made on (gathered from the URL). And since a Publication is a site, in a specific language, it is called a localization, and not just a Publication (DXA uses strongly typed models, not the CMS domain model).
Note that if you want to figure out how DXA is working internally, it absolutely makes a lot of sense to try to build it from the source code and running a debug in Visual Studio. But even just loading all the source code in Visual Studio will help you to jump from the code into the classes used there etc. And feel free to suggest aditional documentation (preferaly in XML doc comments) as a pull request to things which we haven't made clear enough (or just log an issue if you can't figure it out).