It seems fine to consider those adjuncts. Why wouldn't you? Remember that complements are usually important parts of the phrase that are required and unique. To me, those seem to be adjuncts, but that criteria. Do you agree? Your book should have more specific tests you can apply, but the basic idea is somewhat intuitive once you understand the difference.
As for an idiom, you have two choices:
1. Treat it as a single lexical item, equivalent to a word.
2. Ignore the idiomatic meaning and treat it as the normal words in their literal structure. ("It's raining cats and dogs" would be like "It's raining water")
(1) can always work, but it's not a very good answer; (2) only works if the structure makes sense literally. Some idioms are syntactically odd as well such as "attorney general", which has the French word order, so it would require allowing an adjective after a noun, not a usual combination in English. We could add a new rule, or try to reinterpret the syntactic categories of the items, etc. The easiest way is to just call it an exception. But generally for a homework problem it's best to try to be literal and show that you understand the structures, even if the semantics doesn't quite line up.
