Answer:
1. The present participle in the sentence provided is C. "flying".
2. The participial phrase in the sentence provided is B. "Clapping wildly".
3. The word that the participial phrase modifies is "cat".
Explanation: A present participle is a non-finite verb form that ends in -ing. It is generally used to form progressive tenses; however, it can also function as an adjective. For example, in the sentence "The geese flying by are headed south for the winter", "flying" is describing the noun "geese"; therefore, "flying" is a present participle functioning as an adjective. Moreover, a participial phrase is made up of a past or present participle and modifiers/complements. Participial phrases are usually found at the beginning of a sentence. In that way, "Clapping wildly" is a participial phrase ("clapping" is a present participle and "wildly" is a modifier). Finally, the participial phrase in "Hearing the footsteps of its owner, the cat jumped down from the kitchen countertop" is "Hearing the footsteps of its owner" and it is describing the subject of the sentence, that is to say the noun "cat".