Maybe I'm mistaken but shouldn't the version "сделана" also be accepted? The sound is the same. Could be grammaticaly correct if spoken, let's say, about a toy: "От куда эта игрушка?- Она сделана в Китае." I know it was meant "made in..." but still if you are doing a listening exercise it should be correct, in my opinion. (Not reporting yet- I'd like to hear a confirmation from a native speaker first.)
Well, it could be used this way in a context, but «сделано́ в Кита́е» is some kind of cliche used when there's no context, e.g. on various products.
Does the label ever agree with the gender of the object it's labelling, or is it always сделано́ on everything?
Objects do not bear genders, only their names (nouns) do. The phrase stays in the neutre, because it is usually displayed without naming the object. Besides, it is always possible to call an object several names. And "это" (neutre) is always one of them. (I am not a Russian speaker, but a speaker of a language with genders.)