Is there an English grammar equivalent of the Italian "complemento"
Solution 1:
The Italian Wikipedia appears to call both complements and adjuncts complementi. Therefore I conclude that an Italian complemento is a very broad category, and it is not the same as an English complement. I'd call it a constituent. The Italian list includes both complements, like subject and object, and adjuncts, like adjuncts of time and location.
Complementi essenziali e circostanziali
Under this sub-header, it explains that there are complementi that are essential (essenziali) to the structure of the sentence, and those that are not (circostanziali).
In English, a complement is a part that cannot be left out, while an adjunct (also called satellite) can be left out without too much fuss.
I like pigs.
Here, pigs is the object to the verb like: it is essential and a complement. I like is not a grammatical sentence, because the object cannot be left out.
I like pigs sometimes.
Here, sometimes is an adverbial constituent of time; it is not essential and hence an adjunct. Note that the distinction between what is essential and what isn't is not always clear: the categories complement and adjunct/satellite are by no means clear cut. There is often debate about various practical examples.
Since the Italian word seems to include both complements and adjuncts, it must signify a constituent, which is basically a building-block in a sentence that has its own syntactic function. The above sentence has three constituents: I, pigs, sometimes. Subjects and object are complements; constituents of time are mostly adjuncts (but not always).
Many of the examples in your question are adverbial; some are adverbial adjuncts, others adverbial complements. Note that adverbial constituents are usually adjuncts.
Solution 2:
From looking at Wikipedia's page on adverbials, I gather that any complemento is also an adverbial; in your examples, either an adjunct or an adverbial complement. Wikipedia says:
In grammar an adverbial is a word (an adverb) or a group of words (an adverbial phrase or an adverbial clause) that modifies or tells us something about the sentence or the verb. The word adverbial is also used as an adjective, meaning 'having the same function as an adverb'. Look at the examples below:
Danny speaks fluently. (telling us more about the verb)
Lorna ate breakfast yesterday morning.[...]
Adverbials are typically divided into four classes:
adverbial complements (i.e. obligatory adverbial) are adverbials that render a sentence ungrammatical and meaningless if removed.
John put the flowers in a vase.
adjuncts: these are part of the core meaning of the sentence, but if omitted still leave a meaningful sentence.
John helped me with my homework.
conjuncts: these link two sentences together.
John helped so I was, therefore, able to do my homework.
disjuncts: these make comments on the meaning of the rest of the sentence.
Surprisingly, he passed all of his exams.
About adverbial complement:
An adverbial complement is an adverbial that is obligatorily subcategorized for by a verb, such that if removed, it will yield an ungrammatical sentence:
- She put the cheese back.
- *She put the cheese.
Adjunct:
In linguistics, an adjunct is an optional, or structurally dispensable, part of a sentence that, when removed, will not affect the remainder of the sentence except to discard from it some auxiliary information.
[...]
An adjunct can be a single word, a phrase, or a clause.
Single word
She will leave tomorrow.
Phrase
She will leave in the morning.
Clause
She will leave after she has had breakfast.