Here, 'as' introduces a dependent clause ('I say'). It functions as a subordinating conjunction.

'As' is followed by a noun phrase 'a waiter' and indicates a role. It functions as a preposition.

'Next' modifies the verb 'saw' (meaning 'the next time'). It is an adverb.

'Next' modifies the noun 'week'. It is an adjective.

Here, 'round' refers to a unit of the game. It is a noun.

'Setting' modifies 'sun'. It is a present participle acting as an adjective.

A partitive noun is used to count or quantify uncountable nouns. 'Slice' quantifies 'bread'.

'Waiting' describes the state of 'me' as maintained by the subject. It functions as a present participle (objective complement).

'Sound' is the action to be performed (to cause to make a noise). It is a verb.

'Sound' is the thing being described (the subject). It is a noun.