How to import specific text/line under headings in Google doc to Google sheet using google apps script?

There are a couple of assumptions for this script:

• There is a finite number of header styles you're using (e.g. 'Header 1' and 'Header 2' in my example below)
• Your questions always contain 'QUESTION'
• There is no other text apart from the headers and the question lines (but if there is, in principle it will be skipped)

In that case, the below code will work:

function getHeadings() {
  var pars = DocumentApp.getActiveDocument().getBody().getParagraphs();
  var currentHdg = "";
  var questions = [];
  for(var i=0; i<pars.length; i++) {
    var par = pars[i];
    var text = par.getText();
    var hdg = par.getHeading();
    if (hdg.toString().indexOf("HEADING") > -1){
      currentHdg = text;
    }
    else if(text.indexOf("QUESTION") > -1){
      questions.push([currentHdg,text.replace("QUESTION","").trim()]);
    }
  }
  Logger.log(questions);
}

You can then format questions into the table output format you need.

Edit: I have updated my answer to cover all heading types.