Quiz allowing move to next slide without answer

I think you may be confusing how the Quiz > Settings > Required options work.

If you set it to User Must Take the Quiz to Continue, that only means they are forced to attempt the quiz as a whole before being allowed to proceed beyond the Quiz Results slide.  It doesn't force them to answer each and every question.  There is another Required option that does that.  It's called something like User Must Answer Every Question.

I think you messed up the embedded features of the question slides. Have a look at:

Question Question Slides in Captivate - Captivate blog

Personally I will never allow Backwards movement at all in a quiz. If you do that, you can drag the Next button under the Clear button. The Next button has a double functionality: during the Quiz it acts as a Skip button and that is what you do not want. During Review it acts as a Next button. If you do not use Review, you don't need the Next button. If you want Review, dragging the Next button under the Clear buttons solves the problem: during Review both Clear and Submit button will disappear and the Next button will be come available.

I cannot see directly what happened with the actions that are not executed, unless you have another shape button on the question slide that pauses after the pausing of the Submit button.

Your setting 'Required....' can cause problems as well, especially since you allow free navigation within the quiz (and outside) with the Back and Next navigation.

Please, try to read that blog post, and if you have more questions, will try to answer them.