Yes, the correct adverb is comfortably. In this sentence, is resting is the action verb.
The helping verb is is.
Yes, the correct answer in this case is "comfortably." Even though it follows the linking verb "is," the adverb "comfortably" is modifying the verb "resting" by describing how she is resting. In this sentence, "comfortably" functions as an adverb, indicating the manner in which she is resting backstage.