1. For a holiday abroad you need a valid passport. (adjective)
Since we don't say: *an abroad holiday and you might ask the question 'A holiday where? Abroad! and you could replace 'abroad' with 'in China' I would call 'abroad' here an adverb.
2. We prefer imports of cheap food (which come) from abroad/Africa/China. (noun) But it's in the prepositional adverbial 'from abroad'
You are right: just because we call a word a verb or a noun or whatever, that is no guarantee that it will have that function in every sentence. But you know that well from Chinese!!
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