I think your i)-iii) are adverbs, but I don't agree about what they modify. I don't know about iv).
In i), it is the event of the man leaping, described by a sentence, which is modified by being said to be sudden. So "suddenly" modifies a sentence.
In ii), it is the inception of the state of Alice being afraid, described by a sentence, which is modified by being said to be sudden. So "suddenly" modifies a sentence. (Alternatively, perhaps it's the state of being afraid expressed by a verb phrase which is modified.)
In iii), it's the temporal relationship of two events that "when" concerns, each of the events described by a sentence: The grunions come ashore [at a certain time], and We all feast [at that time]. So the adverb "when the grunions come ashore" modifies the sentence "we all feast".
This is something that traditional grammarians are not good at, because somehow they've gotten the idea that modifiers always modify words. Often, adverbs modify phrases. In the typology of adverbs offered by McCawley in The Syntactic Phenomena of English, the only clause adverbs that modify verbs are adverbs of extent, such as "completely".