Javascript - radio buttons onlick not working

I am stuck with a problem. I want to add call functions based on selection in radio button. But one of radio buttons doesn't work at all (not calling the function), other is not checked when clicked. Here is my code:

  function clearElement(element_id){
    document.getElementById(element_id).remove();
  }

  function createCheck(){
    if (!document.getElementById('check')){
      var btn = "<button onclick=\"checkData()\" id='check'>Check</button>";
      document.getElementById("added").innerHTML += btn;
    }
  }


  function addElements(){
    var added0 = "<p>Choose the filling method:</p><br>";
    var added1 = "<input type=\"radio\" value='Auto' id='auto' name=\"auto_manual\">I have ID</input>";
    var added2 = "<input type=\"radio\" value='Manually' id='manual' name=\"auto_manual\"> Enter data manually</input><br>";
    var added3 = "<p>Identification Code</p><br><input type=text id='ID'><br>";
    var added4 = "<p>Enter your email address:</p><br><input type='email' id='mail' autocomplete=\"on\"></input><br>";
    var added5 = "<button onclick=\"fillIn()\">Continue</button>";
    document.body.innerHTML += "<div id=\"added\">" + added0 + added1 + added2 + added3 + added4 + added5 + "</div>";
    var f0     = document.getElementById('auto');
    var f1     = document.getElementById('manual');
    f0.onclick = function() { createCheck();};
    f1.onclick = function() { clearSelect('check');};
  }

I want it to work the following way: if a user chooses "I have ID" option, the radio button is checked and the button "Check" will be created. If "Enter data manually", the button "Check" will disappear if exists.

Could you, please, help me with it?

Update (HTML):

<!DOCTYPE html>
<html>
  <head>
    <base target="_top">
    <title>Demo Web App</title>
  </head>
  <body>
    <h1>Template Creator Bot</h1> <br> <br>
    <script>
        ...
  </script>
  <div id='change'>
    <select name="docs" id="selectedTemplate">
      <option value="Order">Order</option>
      <option value="Complaint">Complaint</option>
      <option value="Other">Other</option>
    </select>
    <button onclick="addElements()">Next</button>
  </div>
  </body>
</html>