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//1. The code you have included in hd7b.js is perfect.

//2. On the login page, you should change the code to the following:
<script type="text/javascript">
  jQuery(document.getElementById('input_email')).blur(function() { // Replace with the ID of the HTML input element where they enter their email
      var input = $(this); 
      var email = input.val();
      var regex = /^([a-zA-Z0-9_\.\-\+])+\@(([a-zA-Z0-9\-])+\.)+([a-zA-Z0-9]{2,4})+$/;
     
      if(regex.test(email)) {
        _veroq.push(['user', {
          id: email,
          email: email
        }]);
      }
  });
</script>

//...also remove this:
<script type="text/javascript">
  _veroq.push(['track', 'begins checkout']);
</script>

//3. On the viewed product pages, you are not including hd7b.js, hence it's not recording the event you're tracking?
 
//4. On http://www.tim-und-lucy.de/shopping_cart.php I would do something like:
<script type="text/javascript">
  var products = []
  //Iterate through all products in your cart and do:
  products.push({name: 'product name', url: 'link to product', image_url: 'link to product image'});
  _veroq.push(['track', 'begins checkout', {products: products}]);
</script>

//5. On the thank you page, after checkout, I'd do something similar:
<script type="text/javascript">
  var products = []
  //Iterate through all products in your cart and do:
  products.push({name: 'product name', url: 'link to product', image_url: 'link to product image'});
  _veroq.push(['track', 'completes checkout', {products: products}]);
</script>