The answers are the following:
9. D. gerund
Gerunds are action words but considered as a subject of the sentence. it has a specific form which is verb+ -ing.
10. B. participial.
Participles and gerunds are similar with their form, which is verb + -ing, but they differ by their functions. If gerunds are used as a subject, participles are used as an adverb or adjective.
Your correct answer is the fourth: 'After they rested a few days, the aliens revived sufficiently to explore.'
Answer:
option B is the correct answer