There is a lot of confusion about qualitative and quantitative research. The difference between them relates to the type of things you are trying to find out, not the type of questions you ask.
Open-ended questions, where people provide answers in their own words, are used in both quantitative and qualitative research. Even the National Census uses some open-ended questions and you cannot describe that qualitative research. Just because you are asking open-ended questions doesn’t mean you are doing qualitative research.
Quantitative research is about counting or measuring things - about how much, how many, how frequently, when and where. It involves collecting a relatively small amount of data from a lot of people – usually 100s to 1000s.
Quantitative research always involves some statistical analysis of the data, even if only averages and percentage frequencies.
Qualitative research is about exploring in detail why and how things happen - their causes, sequences of events, outcomes. Qualitative research is about collecting a lot of data from a small number of people – usually between 10 – 100. Qualitative research very often involves using open-ended questions but also other techniques including closed questions and observational techniques.
Qualitative data is immensely rich in detail so it needs to be carefully collated and analysed. This will take time. You cannot just dump raw qualitative data into a report and expect readers to make sense of it. For more on this see How to analyse data from open-ended questions and How to analyse data from observations.
Whether you use quantitative or qualitative research depends on the type of information you are trying to obtain. Are you trying to assess how frequent or widespread something is - if so that’s quantitative research. If you trying to understand in detail why and how something happens – you need to conduct qualitative research.
In many cases it is worth doing a bit of both – qualitative research to explore in depth what is happening and why; quantitative research to assess how often and among which audience groups this is occurring. But you will be using different techniques and different samples of your audience.
Quantitative research is also a useful way of cross-checking the reliability of your qualitative sample i.e. whether the qualitative research findings correspond to the feedback from the much larger quantitative sample?