What's wrong with "There are birds in a forest"? One wouldn't say that very often, but grammatically speaking, wouldn't this suffice?
A poem commenting on the meaning of life and it's relation to social media: There are birds in a forest/ And people in a city/ All they do/ Is tweet, tweet, tweet
I agree. I reported it. Word order mostly changes emphasis in Russian. The new or important information goes at the end of the sentence. The birds are in the forest could be В лесу птицы or Птицы в лесу depending on the emphasis intended. That being said, "there are birds in the forest" could also be a correct translation depending on the speaker's meaning, for example, a general statement indicating that there are birds in the forest. В лесу есть птицы, on the other hand, might be the answer to a question like "что есть в лесу?" Again, the new information is at the end of the sentence in the answer.
I believe the notes should have something on the Locative (also known as the 2nd Prepositional). Basically, you always use it with certain nouns (verbs have nothing to do with it) when talking about physical or temporal location with the prepositions «в» and «на». So, for example, «быть в лесу́», but «говорить о лесе», «лежать в снегу́», but «думать о снеге». There is a set of about 150 nouns that use the Locative, some can be found here.