How do you remove header and footer in Word 2011?
I don't think I've ever seen the None option you're referring to. Even in Ms Word 2016 there's no such option, but you do get a Remove Header option.

As for MS Word 2011, the only way I've ever been able to remove a header is as follows:


Double-click on the header within your document
Go to Edit > Select All (or just press the command A keyboard shortcut)
Now press the Delete key on your keyboard
Click the Close button on the header (see image below):




Now your Header will be gone.