...или двух мух одной хлопушкой :)

I think, it would be better to separate these sentences in two differents entires.

Please, check the French and Dutch translation.

The sentence is «One stone — two butterflies».

I've deleted an explanation in parentheses «Убить двух зайцев одним выстрелом» (To kill 2 hares with one shot). I'm not sure if we have to add it as a separate sentence: it was not a full sentence.

Is this an idiom in Russian?

It depends - is this a litteral translation from the Japanese or is it actually used as an expression in Russian? In Dutch it's a saying ("to hit two flies in one slap"), so if it's not a saying in Russian (as I suppose), it would be more appropriate to translate it more or less litteraly in Dutch.

Instead of just adding the deleted phrase as such, you could make a complete sentence with it. :)

It's not an idiom, but idioms shouldn't be necessarily translated by idioms. :)

At least, it's a full sentence (though consisting only of nominal clauses), and it can be understood by a Russian speaker (at least I believe so).

If we were use a natural Russian idiom, we have to add some context. E.g. «we killed 2 hares with 1 shot».

I know idioms don't necessarily need to be translated by idioms, but still, I think this Dutch-Russian pair is rather useless, especially since the Russian sentence isn't something that is typically said like that by Russian speakers. :) So I split of the Dutch phrase and made a comlete sentence with it. Please check the Russian and English translations.