Oh, I didn't know that the file extension could override the doctype
On a *nix system, they can't, because they don't mean anything special. Like XHTMLcoder, you could have a foo.kangaroo file. Files are files, on *nix (though some applications may prefer to guess what a file type is based on extension). I could have HTML files on my server with no extension at all. So long as I set them to the correct MIME type and tell my server what to do with them, all's good.
But the headers the server sends out with the pages... that matters, exactly as Jeff Mott showed. How the server serves the page will override the meta tag (the meta tag is more of a fallback... for those nasty times when someone did not set up their server properly and it's sending out pages without headers stating what the MIME type is).
If your server does change which MIME type it associates your page with based on file extension, and you're not using a Windows server (I could be wrong, but I understand that on Windows, file extensions do mean something), then it's just a setting on your server to guess your intended MIME type. But that's a server setting, and not any kind of general rule about file extensions.
Nah, not really. I think when everyone realised what a pain XML was, the world moved on and XHTML will be used for those who actually have a use for XML and find using it also for their web stuff makes sense. Everyone else will have moved on to JSON I think
So it's not dead, but it's not something most of us have any real reason to use, other than personal preference.