First, although it may be out of the questions,I think it is an important part to find out the original question of the answer.
From where I stand,the sentence "They learn English as an international language" is really difficult to understand.
I know English is an international language,but can we learn it "as" an international language?
In such a case,"as" means similarly "to be".
For example,I acquired a lot of skills as a way to show myself.
In this case, acquiring skills has something to do with a way to show myself and,of course, "as" can be replaced with "to be".
Thus,your sentence can be seen as "They learn English to be an international language" and that's why it seems odd to me. International languages have nothing to do with learning them！
The word "as" in this sentence can be seen as "to be",so, actually,we can just use "to be" instead of "as" to make questions understood.
But,if we change the sentence into other meaningful sentence like"They learn English as a manner of communication",the question can be more exact sentences like "why do they learn English?","what is an intention of learning English for them?" or "what do they learn English to be?"
I'm not a English speaker,but I hope this answer can help you.xd