No for two reasons. One is that neither English nor German usually speaks of vacation in the plural, unlike Spanish and perhaps some other languages. The second is that the German word is in the singular so you would translate directly. Only if you were translating from a language which normally refers to vacation in the singular like either English or German to a language that generally refers to vacation in the plural like Spanish would you change from singular to plural in the translation.
In verifying American use, we would use vacation. Holiday would be used only for a specific day of celebration (though around Thanksgiving and Christmas, 'holidays' may be used to denote a larger time span). While holiday often implies removal of responsibility from school or work and potential celebratory activities, vacation often implies a trip. However, it is possible to vacation from home without a trip. Clarification is usually given for this though.
That's because Duo uses American English as the standard. In American English a holiday is a bank holiday or government recognized day but not a vacation. I know that Duo's has made some adjustments for British English, but they are slow to get introduced and generally only encompass things like accepting some British spellings and perhaps words like lorry which have no meaning in American English and are fairly well known as British words. I don't think differences that can potentially affect the meaning when interpreted in American English are likely to be accepted. That is essentially the purpose of using a standard: providing a framework for understanding and interpreting the translation. Of course the problem on both sides is that few people really are aware of the full scope of the differences between British English and American English.
Actually the British do speak of going on Holiday when they speak of vacation. It is the singular form. But as Holiday means one day to Americans and holidays generally means the time between Thanksgiving and New Years or at least Christmas and New Year, it would be a bad idea to accept the word. If you base your program on American English and accept a British construction that has a totally different meaning in American English, it would be confusing.
The meaning here is essentially the opposite of what you wrote. You always have to remember what English does to prevent double negatives. Most German sentences which form a negative with kein instead of nicht have two possible translations. For this sentence they would be I want no vacation or I don't want any vacation. That's the bottom line. Kein and its various case forms is a negative. It means no or none or not any. Any without the not is a positive. So saying you want any vacation is saying you will take as much as you can. My other question is holidays. I am an American, so I might be wrong, but my understanding is the British use the single form of the word holiday to mean what Americans mean by vacation, which is what Urlaub means. Holidays are multiple days celebrating particular religious or political events. That would be Ferien or Feiertage.
Hi Lynette, thanks for your reply. I knew what it meant literally; I was looking for a more natural English equivalent but I take your point; we've always talked about going on vacation, meaning having time off. (Thinks - I wonder how they would interpret gardening leave!!)