Translation:Have you been to a foreign country?
Literally this sentence does mean Does The Case That You Went To A Foreign Country Exist? It is asking whether you have such experience. But in English you would never express it in the same way. You would rather say Have You (Ever) Been To Any Foreign Country?
あります can also mean something close "have" as in this case's "have been."
外国 Is neither plural or singular, but both.
こと turns 外国に行った into a noun meaning something like "went/been to foreign country/countries."
Therefore, writing 外国 に 行った こと が ありますか translates roughly to "been to foreign coutries, have you?" or more appropriately "Have you been to foreign countries?"
The point is that it's silly to try to translate exactly what you're reading to English based on strict word-for-word translations. It doesn't work. The translation of any given word or phrase should be organic depending on the situation, makeup of the sentence, etc. Any language will be like that.
Keith, your last sentence is awkward and not great English. Better options: "have you ever been to a foreign country?", or (the far more commonly used phrases) "have you ever been overseas?"/"have you ever been abroad?".
You are right. In this case, using hiragana is correct. More info: https://m.chiebukuro.yahoo.co.jp/detail/q1013194790
This is why many Japanese people mix up past tense and present perfect. There is no verb tense for future or present perfect in Japanese, so the common link here is "experience".
English = Have you ever + past participle Japanese = verb [ta] + koto ga arimasu ka (as a question)
The more you study Japanese as an English native speaker, the more you'll be forced to rely less on English, as they'll be less equivalents....
'Overseas' would only apply if you live in a waterlocked country. 'Abroad' is a better expression.
This English suggestion is totally not idiomatic. I wrote "Have you been to any foreign countries?" which was rejected. But we would always say "a foriegn country" or "any foreign countries" (or "abroad"). Duolingo keeps making it impossible to get a 100% lesson without memorizing irrelevant quirks...
What is incorrect about my answer 'Did you go to a foreign country' ?
"Have you ever been to a foreign country?" feels somewhat more natural to me, and highlights the intention of ことがある more.
You don't need the preposition "in", so it would be "have you been overseas?"