Update names of WebSite projects for consistency

Project/Assembly names are all like 'FeatureWebSite' root namespaces
updated accordingly. This makes processing all of the functional tests and
deploying the web sites much simpler.
Update WebAPI shim functional tests to use a header for payload

The issue is that responses to HEAD cannot have a body. When running these
tests on a real server, they break because the server throws when you try
to write to the body.