To partially answer my own question:
I call the fields in my position override with
<?php echo $cck->renderField('field_name'); ?>
The openeing and closing <form> tags with the correct attributes get added automatically, also the hidden fields and the javascript for submission. So the form is working :-)
But in seb_minima the labels do not get rendered together with the fields.
So I added for every field where I want to have a label:
<label><?php echo $cck->get('contact_surname')->label; ?></label>
But here the asterisk * for required fields doesn't get rendered.
How can I get the complete fields rendered with labels that show the * for required fields?