It is not archaic at all. Here in Canada it is the polite register you'd use for example to ask a shopkeeper, and "Have you dresses and coats?" sounds like a perfectly reasonable question to ask a shopkeeper! (I wouldn't use it talking to friends for example, unless I was visiting a friend at their house for the first time and asking something trying to sound polite, like "have you any tea?")
Is jas strictly a suitcoat, or is it used for any coat, like a winter coat? Also, I think "have you..." should be an acceptable construction for these types of translations, so I reported it. Although I rarely hear it in American English, I like to translate "hebben jullie..." to "have you..." or "have you all..." because it helps me to think in Dutch, so to speak.
Do you have? ‧ ‧ Have you? ‧ ‧ Have you 827 M hits •
Have you no wit, manners, nor honestly but to gabble • W Shakespeare • Twelfth Night • Act II, Scene III, Pg 5 • Have you a teacher's certificate • Have you any wool / meat / rooms • Have you some xyz • Have you no xyz; sense, shame, decency, pride, honour, water, & etc.
For me it doesn't sound like that, but even if it did, I think it could well be in the normal range of Dutch pronunciation. What you are expecting is basically the only normal pronunciation of j in German. But Dutch is more similar to English than German is, and it has a stronger French influence than German does, so i would expect a tendency towards [ʒ].
In this case yes. Questions, like other sentences, typically start with what is most important. In a question that has a question word ("wh..."), that's the question word. In a yes/no question (such as this one), that's the verb. Just like in English, except in English the first word in a yes/no question is typically do.
The construction with do is called "do support". It is required in questions for full verbs in Celtic, English and very few other languages. In other Germanic languages such as Dutch and German, do support can often be used colloquially or in dialects, but it is considered wrong in the standard language.
English speakers disagree with each other about whether do support is required when have is used as a full verb. This is because do support once wasn't required at all (and in fact was wrong!), and is still wrong for auxiliaries. Since have can also serve as an auxiliary, use of have as a full verb is one of the last cases of full verbs not requiring do support -- for some but not all speakers.
For some English speakers, "Have you dresses and coats?" is still grammatical. Others consider it wrong and insist on saying "Do you have dresses and coats?" (treating have as a full verb) or "Have you got dresses and coats? (avoiding the issue).
So long as the other two variants are also accepted, there is nothing to fix.