The quizzes for your online course may include many different types of questions including: multiple choice, true-false, matching, short answer, long answer, etc. Quizzes will definitely have a due date, but they also may have time limits or other restrictions that your instructor has set. You can and should "save" your answers to questions as you progress through a quiz, but saving is not the same thing as turning in the answer. It is important to make sure you "submit" your quiz when it is complete.
Once you have submitted your quiz, it may be automatically scored in which case you can check your "submission" immediately to see how you did and often to see which questions you answered correctly or incorrectly. Some quizzes may have to be manually scored by the instructor. Be patient! Remember, an instructor may have to score quizzes from multiple classes.