The word that best replaces "anxious and unsettled" in the sentence is "agitated."
The word "agitated" means to feel anxious, restless, or upset. In the context of the sentence, the boy is expressing that his heart is restless and emotional because of his dreams and his passion for a woman of the desert. Therefore, "agitated" is the best option that accurately conveys the meaning of the sentence.
None of the other options - "luminous," "monotony," "melancholy," or "prognostications" - accurately convey the idea of being restless, anxious, or upset.