Not any more. (Link to enabling CORS on server: http://enable-cors.org/)
Not any more.
Yes.
Annotated code example: http://jsfiddle.net/m1erickson/gz6e8/
Once you have properly configured your server for CORS you can download an image that won't taint your canvas like this:
var img=new Image();
img.crossOrigin="anonymous";
img.src="http://yourConfiguredServer.com/logo.png";
Illustration of the results: