1. Nope, it's FileCutter (which is not an application but a contextual menu plugin.) However, I see now it doesn't work on Snow Leopard.
http://www.versiontracker.com/dyn/moreinfo/macosx/29931
5. It's not inconsistent if you quit applications. Just right click the dock icon and click Quit, it will
always kill the application. Why the close button behaves like it does has been explained. But there is no need to close applications with 8GB of RAM, that would be pure waste of that memory.
About inconsistency, in Windows the close button can be just as inconsistent as in Mac OS X. Internet Explorer shuts down when you click it. Windows Live Messenger minimizes to the system tray. I'm sorry, but the close button does whatever works best for that particular application, that's the way it works in pretty much all operating systems.