Is the prohibition of using an IUD as a contraceptive based on the impermissibility of a non-mahram seeing a woman's awrah—even if she is a doctor—or because it is considered killing a soul? And if an IUD has been inserted for a long time, must it be removed immediately because it is forbidden?

A woman inserting an IUD is forbidden due to a non-mahram seeing her major 'awrah, not because it is considered feticide. If a woman inserts it herself, or her husband inserts it for her, there is no harm in it, as long as no damage results from it. It is not obligatory to remove it unless its continued presence causes harm.