Can a guest to website leave new quastions to quiz?

Hi Nikita,
the short answer is no, you cannot do this, but it’s possible for you (or a WordPress developer if you are not one) to build this in if it’s something you really need.

Just note that the reason I don’t have this functionality is that A) allowing random non-authenticated users to write to your database is inherently less secure, and B) moderation would be a nightmare. HD Quiz does not have “published” / “draft” states for questions, so a whole new system would need to be created to allow you to manually approve submitted questions.

My Recommendation

Since you need to manually moderate and approve submitted questions no matter what, I recommend using a form builder such as HDForms (or any other contact form plugin) to build a contact form for users to submit questions. You can then review and add any questions you want manually. It won’t be as simple for you as clicking on an “approve” button (like with WordPress comments), but it will work for you right now, and you don’t have to worry about security!