So, there are a few things going on here. First, "Toilet is far away" isn't a complete English sentence -- you need an article for it to make sense ("the toilet" in this case). Second, the Russian word "туалет" doesn't refer to the literal toilet that you sit on (at least in this context), but instead what is referred to in English as the bathroom, restroom, washroom, lavatory, or water closet (among more colorful terms), depending on dialect. This is the room that houses toilets and sinks in a public space. A "ванная" is a room with a literal bath in it -- the thing you fill with water and soak yourself in. If you ask "где ванная?" in a public space in Russia, you are liable to get a very confused look in response, because they'll think you want to bathe (I have had this happen to me before).
Part of the confusion here stems from the fact that in Russian homes, the toilet and the bath are housed in separate rooms, and so are considered distinct from one another. A "ванная" doesn't, by convention, have a toilet in it.
Yes, I haven't seen that I forgot "the". Nevermind that, the issue still stays. I know the difference between туалет and ванная, I am a Slavic language native, but the translation is wrong. Why use bathroom when you can use the word "toilet"? I really don't understand. And I can assure you that I will not ask "где ванная?" for the toilet.
Forgive me if my response came off as condescending or rude. Because this course is being used by people all over the world, including many who are not native English or Russian speakers, I try not to make assumptions about what people do or do not know when answering questions.
To answer your question, you can use "toilet" in English to refer to a bathroom, but it would be considered slightly crass or low class, at least in the US (though the person would understand what you mean). Moreover, for a course ostensibly targeted at English speakers learning Russian, it's important to distinguish between the toilet itself and the room which houses toilets in a public space. If "toilet" were accepted here, it would be liable to create confusion. I imagine this is the logic behind not allowing "toilet" here.
No, it is alright. But, as mightypotatoe mentioned, it is a commonly used term in British English. I personally have a mixed vocabulary of AE and BE, because of a different influences through my life. Anyway, in my humble opinion, "toilet" should be the right answer also.
The default for this course is American English and in American English "bathroom" and "restroom" are the words most commonly used to refer to the public space where toilets and sinks are housed. This is probably why the number one solution is given as "the bathroom." "The toilet/toilets" should still be accepted, however, since it is a commonly used term in British English.
If "bathroom" seems like a strange word to use to refer to the public toilets, simply accept it as a quirk of the American English dialect and use "restroom" instead.
It sounds like daleko to me, and that's all I've ever heard from real live speakers too, so I'd recommend saying it that way too.
I have a hypothesis that when learning a new language, if it's very different from any you know, before you can understand it, you not only need to know the meanings of words, you have to learn to hear the language.
In my case, I suspect it has to do with the sounds of letters in my language. An American 'A' is an 'E' in my language. So we'd get amusing things like 'E' as in 'Apple'. I don't generally think about sounding like a native American speaker when writing down sounds, but for this website, it might not be a bad thing.
I definitely agree that learning how to hear a language is an integral part of learning how to pronounce it.