Translation:She's sick, she is sleeping in the room.
I hate to tell you this, but the phrase "she is sleeping in A room" (vs. 'THE room) is not natural English and should be marked incorrect in this context. " She is sleeping in A room" (capitalization here is mine, for emphasis) is equivalent to saying that she is sleeping in 'some/any' room, and sounds comical or sarcastic. It just isn't proper English. It is theoretically possible to say 'a room' in this sentence, but it is very difficult (for me, as an educated native speaker of English) to imagine a context in which that choice would apply.
It is improbable but it is not incorrect.
You just gave a context where someone would say it.
Here's another one: There are a bunch of people at a party in a large house. The sick, sleeping person does not live there, and neither do you or the person who asks you, "Hey, where is Julie, did she go home?"
Here's yet another one: We're at a clinic with several exam rooms. It's not a busy day, and the sick person was mainly just exhausted, so we let her take a nap in the room she was examined in. You are reporting to the family member who brought her in.
Jieke is quite right. Here, an English speaker would say 'the room', 'her room,' 'the bedroom,' 'the back room,', etc. We would never say 'a' room without explanation unless it is a context where we do not know which specific room, for example: "I need to reserve A ROOM at the conference hotel," or I need to " get Mom A ROOM at the hotel." In those cases, we're saying [need to get] "A/ANY room, I. e. we do not know which specific room or don't care.
She fell sick
She has contracted an illness
She has grown ill
She got sick
She became sick
... there are many ways to put this.
I think the 生病 is referring to contracting or incubating an illness (which to us seems unnecessarily medical and technical perhaps ...but if you look for it we have these in English too).
It does apply to both location and action that is occuring. If 在 is before a verb it indicates an action in progress. If you are using the PC based course, the tip is in 'Weather'. So in this case it should be for location. I believe your answer was marked wrong because it is not the wording they want.
I could swear I've heard 房间 used to mean one's apartment—sort of like turn of the century English referring to one's "rooms." I get that it's the more direct, first sense in the dictionary meaning, but am I wrong to think this would be a valid interpretation? Beyond that, the 'correct' English answers here often remind me of Chinese-style English—the way that people back in China were taught was correct, but isn't really natural for a native speaker. I'm also getting a bit miffed with the comma splices and such in the 'correct' answers.