Basically, I'm looking for methods that, instead of running detailed Interviews with few people, aggregate similar answers by asking many people few very basic questions.
Is there something established in Sociology, Psychology?
Are there any method to aggregate a bigger picture by breaking it down to simple yes/no-questions?
If you are doing a qualitative research through detailed interviews with few people, you need to ask open ended questions then aggregate their answers into key themes. If you ask closed questions like "yes / no" etc., then you will get similar answers. It is not a norm in qualitative research to ask many people as the focus is on qualitative data collected & not quantitative data.
If you need to ask many people with certain questions for quantitative research, you can conduct a questionnaire survey. However, there is a methodology you need to observe how to adopt / adapt / develop your own questionnaire for survey.
As Han and Julian point out - you need to use a quantitative approach for your needs. Closed answers, as Han notes, ask for a simple yes/no response but you can use a mix of open and closed questions in a questionnaire.