The Open and Close dates determine when the quiz is available. If you do not select the Enable checkbox for Open the quiz, the quiz will be permanently open, instead of becoming available on a given date. If you do not select the Enable checkbox for Close the quiz, then once the quiz is open and will stay open permanently instead of becoming unavailable on a given date.
If you want to hide a quiz, further down on this page, under Common module settings, you will see the Visible setting; change this setting to Hide.
By default, a quiz ...