Using JavaScript to interact with tables and fields

You questions is a bit broad but I will try to answer.

The most common way to "interact with table and field" is to (1) perform an AJAX request using the QuickBaser HTTP API and (2) process the XML response. Historically this is done using jQuery because jQuery is already loaded in QuickBase's pages but these days everything can be done with raw JavaScript. Here is an example of typical code entered manually into the console to query the formula function table for all records with [Category]="Type Conversion":

(function(){
  var dbid ="9kaw8phg";
  var dbidTable = "6ewwzuuj";
  var apptoken = "not required";
  $.ajaxSetup({data: {apptoken: apptoken}});
  $.get(dbidTable, {
    act: "API_DoQuery",
    query: "{6.EX.Type Conversion}",
    clist: "3.7.8"
  }).then(function(xml) {
    console.dirxml(xml);
    $("record", xml).each(function() {
      var rid = $("record_id_", this).text();
      var name = $("function_name", this).text();
      var type = $("result_type", this).text();
      console.log(rid, name, type);
    });
  });
})();

I would encourage you to perform this test yourself and explore the console output of the xml response and individual fields.