The prepositional phrase in the sentence is A. to the party.
Adverb describe (modify) verbs and other adverbs. When looking for an adverb, you must first find the verb. In the first sentence, the verb is took. Off is also an adverb, but ask yourself, took off "how"? If you can answer that (with quickly and cautiously), that is your adverbial phrase. From an overnight rain, over the surface, and around the track are all prepositional phrases. Warm and shining are describing the sun, so they are adjectives.
My answer is that it is a poem and not all poems have capitol letters in the beginning of a line but in this one the reason is she wanted it to make more sense