When you create a quiz, all text and images you have filled out will be submitted and republished for the public to see. No additional information is shared with the public. After the quiz is made, you will not have access to any information regarding any quizzes that the public does not have access to. This last part may be optional in the future. Currently, the only featured quizzes are ones that I select manually.
When you take a quiz, all of your responses will be aggregated into summaries that can be viewed on that quiz's analytics page. The public cannot see your individual responses, although if someone knows that you took a quiz, they may infer your responses. Additionally, your final response may be correlated with the model visualization at the bottom of the analytics page, which may be revealing if you are the only one who gave feedback for a particular category.
If there is any information that is sensitive to you, it is advisable to not submit that information. For quizzes with a high amount of responses and feedback, this is less of an issue.
For general website privacy, see this page.