I don't know why the interior lights don't work. Body control module?
Most mechanics use a battery saver (also called a memory saver) when they swap out a car battery to save the radio codes and settings. It's a cheap little gizmo a 9 volt battery plugs into. Don't know why it wouldn't have worked here with the alternator change.
Maybe the service writer at a Mazda dealer could tell you whether replacing an alternator affects the lights or radio.