After nearly going mental for a whole day, I finally found the answer.
The guest self registration form will allow fields to be deleted, but not added to it. In order to add fields which are not there (like the password for instance), it is necessary to select a field which will not be needed in the form (picking a disabled field will do) and click on 'Edit' from the menu underneath.
The options displayed will be related to that specific field, but by simply dropping down the 'Field Name' menu on top, it is possible to select any of the available fields - which will in turn populate the fields below with the correct parameters.
Clicking on 'Save Changes' will then display the new field in the form and 'Enable' will activate it.
Hope it helps,
Giuseppe/