Какая женщина? Why is 'a woman' not accepted?
In my opinion it is because there is mentioned a specific woman who is showing books. That's why there has to be "the".
"The woman is showing (the/some) books to us."
How would you say the woman is showing us our books? нам наши книги?
Why показывает is in present instead of future?? Isn't perfective??
The action is happening right now. Она показывает not покажет (she will have shown/will show)
So показывает is imperfective and покажет is perfective.
Not really. The показывает is imperfective (present simple/continuous) but покажет is future (perfective or not depends on the context)
He will show you the way - Он тебе покажет путь
By 5 o'clock he will have shown you the way - К пяти часам он покажет тебе путь
"books" is code for?