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.
A JAS is used for any coat. We have of course several kinds of coats, to distuinguish between them something is added. Examples. trainingsjas, regenjas, winterjas, zeiljas and for the smaller coats for the kids: regenjasje, winterjasje. 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].
As in "Baa baa black sheep, have you any wool?" For some native speakers of English the answer is still yes (as it was for Shakespeare), for some it is already no. Of course this has nothing to do with Dutch. See my long comment for more details.
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.
So if jurken and jassen were singular, would you have to put an article in front of them?
Yes. In this respect (as in so many), Dutch works exactly like English:
- Hebben jullien een jurk en een jas? - Do you have a dress and a coat?
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.