I am an English native speaker working as a teacher in Germany. When marking my pupils' essays I often encounter the phrase "to do something against something", which is as far as I know simply a direct translation of a German phrase. But I cannot find any answers in my dictionaries. One current example: "The USA never did anything against violence." My gut feelings says the preposition has to be about instead of against here. Is that correct? If not, fine; but further, can against ever be used after do something?
It is alright to use against after do. Against simply means in opposition to, so
The USA never did anything against violence
The USA never did anything in opposition to violence.
On the other hand about means with regard to, so
The USA never did anything about violence
The USA never did anything with regard to violence.
The answer to the last part of the question is clearly that against can be used after do. Never do anything against the law is one example. I never did anything against you is another. Why, then, does The USA never did anything against violence sound odd, when it is certainly grammatical? We can, after all, say The USA intends to act against violence wherever it occurs. The reason is semantic rather grammatical. To do X against Y requires Y to be, at least, a neutral entity. When, as with violence, it has negative connotations, there is a mismatch. Compare The USA never did anything against violence with The USA never did anything against any country that sought peace and stability. In the first, against needs to be substituted with about to effectively convey the intended meaning. In the second, against cannot be substituted with about without changing entirely the intended meaning.
Different prepositions get used in different ways with do. I realize this is not a helpful comment, but at least it's true. Of the Wikipedia list, about seems to me the right single preposition for the cited sentence, though, as noted, against is possible. There is a lot of individual variation on this topic in English, but do something about X is an idiom for pretty much everybody.
The problem is that this do is an Active do, a Pro-verb (analogous to Pronoun, but usually spelled with a hyphen to distinguish it from proverb) that can stand for any semantically active verb (i.e, one that denotes an action, requires an agent subject, and can occur in the progressive construction).
Often some NP appears as the direct object of Active do in order to clarify the action. This is where the Negative Polarity Item anything, triggered by never, fits in; this is one of those places where you can't use something very easily.
Further clarification of do can use prepositional phrases. Virtually any preposition allowing motion, like about, against, beyond, on, and toward(s) can be used to relate the action of do metaphorically to some topic. Some others, specifically targeted at this, include modulo, concerning, and regarding (note that the last two are reduced participles).
Finally, of course, the usual adverbial prepositions can occur here as elsewhere, but are not governed by do specifically, and only indicate where, when, how, etc.
I think whilst using the word against in that context is understandable, it's not the best word to use. Something is telling me against shouldn't be use when discussing an abstract noun (such as love, freedom, happiness). Instead I would use in opposition to, and leave being against for concrete nouns
I can't find a rule anywhere online supporting this, so it's just my gut feeling really.