Grammar

 'Fast' modifies the verb 'ran'. Therefore, it is an adverb here. 

Hard modifies the verb works, describing the manner of the work. Adverbs modify verbs.

Late modifies the verb arrived, indicating when the action took place. Adverbs modify verbs.

Early modifies the noun bird, describing a quality of the bird. Adjectives modify nouns.

Poor modifies the noun man, describing a quality of the man. Adjectives modify nouns.

Outside modifies the verb looking, indicating the direction or location of the action. Adverbs modify verbs.

Fast modifies the noun bowler, describing a quality of the bowler. Adjectives modify nouns.

The word down describes the direction of the verb flowing, functioning as an adverb of place. It does not modify a noun or connect a phrase to another word, so it is not an adjective or preposition.

'Inside' here refers to the inner part of the box. So, it is a noun.

In this context, the word quiet is preceded by the article the, which indicates it is functioning as a noun meaning a state of silence or stillness. While quiet is often an adjective, its position here confirms its noun usage.

Here, quiet modifies the noun life. So, it is an adjective.

The word coward is a person, place, or thing, making it a noun. It serves as the subject of the sentence.

The word late modifies the noun prime minister, identifying which one is being discussed. Words that modify nouns are adjectives.

Nearby is both an adjective and an adverb; howeever, in light of the sentence, it is an adverb because it describe the river as not being far to travel to.

The word inside modifies the noun story, describing its nature or location. Because it modifies a noun, it functions as an adjective.