populating field A with content of field B
In Drupal 6 you could use Computed Field for that, but unfortunately it's not completely ready for Drupal 7 yet.

You could also create a custom module in which you implement hook_node_presave to set the value of 'field A' based on the value of 'field B'. When you choose this method, you may also want to implement hook_form_alter to hide field A from the node form.