Cause and effect refers to an event which causes another event to occur. In that respect, the conjunction <em>since </em>means <em>because </em>or <em>for the reason that.</em> As a result, the expression <em>since the desert air was so dry </em>implies that the aridity of the air in the desert caused the bread to become dry, hard or no longer fresh.
The rest of the alternatives are incorrect because <em>so </em>means very or to a great degree, <em>stale</em> is an adjective that means hard, rancid and unpleasant to eat, and the adverb <em>quickly </em>means fast.
The gerund phrase in this sentence would be "becoming a movie star" because of the verb "becoming" which acts as somewhat of an introduction to the rest of the phrase.