Translation:Birds are singing in the yard.
Chirping and tweeting can be quite the same thing if you sum it to a sound birds do, and if you sum crying as a sound an animal does, it sums up to one word and not entirely different words. I guess that's why in english pokemon games, you have pokemon "cries", maybe this is some sort of direct translation.
Plus, it might be a cultural difference, seeing animal noises as cries is not that wierd, once you detach the emotion.
The difference between が and は is basically that the former INTRODUCES a topic, where the latter BRINGS IT BACK. If you think about it, "the" is usually used before a noun we're familiar with or that we know, whereas "a/an" is used to talk about things we don't know or are not familiar with. "A girl asked me out" / "THE girl asked me out". Hope that helps.
Note I am a native English (American) speaker who's studied Japanese for a couple of years, so I put this all forth tentatively, but with a bit of experience.
「にわでとりがないています」「庭で鳥が鳴いています」 I'd say the で makes it more like "Birds are singing in the yard".
「にわにとりがないています」「庭で鳥が鳴いています」 This is more like "Birds are singing into the yard" [like you sing into a microphone].
で emphasizes the activity being done, while に emphasizes the place (and often implies motion towards a location, though not always. 庭にいます for example, is using に for existence at a location). In this sentence I'd say that に is unlikely because we don't often sing/chirp into something.
There are examples where both に and で are possible, though.
「東京にアパートを買いました。」I bought an apartment in Tokyo. [emphasizing that I am in Tokyo, buying an apartment which is in Tokyo]
「東京でアパートを買いました。」I bought an apartment in Tokyo. [Emphasizing buying an apartment rather than in Tokyo. I think this wouldn't even necessarily imply that the apartment is in Tokyo]
It marked "Birds are singing in the garden" wrong, and suggested "Birds in the garden are singing" instead. (And right now, the translation given at the top of this page says "Birds are singing in the yard.")
My original translation seems fine; I've reported it (Jan. 10, 2018).
EDIT: "In the yard, birds are singing." was marked wrong as well; I've reported it too (1/14).
Can someone explain why this question refused to accept anything other than "A bird in the yard are chirping"? The grammar in that English is horrible. It rejected "A bird in the yard is chirping," and "The birds in the yard are chirping," which are the two things I tried prior. It insists that the singular bird "are" chirping. I reported the bad English and suggested my answers be accepted as of 1/12/2018