Final answer:
In sentence 12, "staring" is a gerund functioning as the subject of the verb "was." In sentence 13, it is also a gerund, but functioning as the subject of the verb "appeared." In sentence 14, "flying" is a present participle modifying the noun "car." In sentence 15, "going" is also a present participle modifying the noun "car." In sentence 19, the sentence has a dangling participle. In sentence 20, "running" is a gerund functioning as the subject of the verb "sent."
Step-by-step explanation:
In sentence 12, "staring" is actually a gerund functioning as the subject of the verb "was."
In sentence 13, "staring" is still a gerund, but now it is functioning as the subject of the verb "appeared."
In sentence 14, "flying" is a present participle modifying the noun "car."
In sentence 15, "going" is also a present participle modifying the noun "car."
In sentence 19, the sentence does indeed have a dangling participle. It is unclear who or what was running across the beach, making the word "flying" a dangling participle.
In sentence 20, "running" is a gerund functioning as the subject of the verb "sent."