Which translation is the more natural one, "He introduces his wife" or "He introduces the woman"?
It depends on the context... if the boss introdudes her secretary, for instance, you use the second option.
OK, I see. But is there a "default" meaning to it if there is no context? What would a native speaker think if he heard only this sentence?
If I heard the sentence I would be inclined to understand it as "the wife". "The woman" sounds a bit rude in this context, if he meant "the woman" I would expect a more polite term like "a senhora" (the lady).
Just listening to the sentence, you hear the article "a" mulher, but without seeing the written version, how can you tell whether he presents the woman or presents to the woman "á" ?
"Introduces" and "presents" can be interchangeable in this context, so "presents" should be accepted - reported