We currently don't have a way to let you require answers, because the entire ethnio screener lives in an overlay, which is a glorified pop-up, and has a long history of annoying web visitors. We don't want to annoy people, and our feeling is that getting an error inside a glorified pop-up would be super annoying. So make your screener short and to the point, and you should get plenty of answers. Remember we automatically filter responses that have more than three blanks anyway.
If you'd like to filter out responses that are missing any specific questions, you can also do that. So instead of putting the onus on a participant to answer every question, we put the onus on researchers to choose the right people. Using the filter bar under "Responses," it's very easy to hide respondents who didn't answer one or more questions.
Lastly, you could state in the invite page that in order to participate, all or certain questions must be filled out. Especially using the "large formatted text block" which will make the warning text as large as you'd like.