Yeah, the lack of article is confusing in this sentence. This rule isn't really explained in the grammar section!
They can have. "Hun har en kjole og sko på" is perfectly valid Danish, in my opinion. You should be able to get by with the same rules as in English.
Hmm, you can't leave out the article before "dress" in English, though. So the rules don't seem to be exactly the same :)
in a very limited case, you can leave out the article in English, for example if you are meaning it like a uniform. EG, he wears wears suit and tie for to work not casual clothes. She wears dress and heels out to dinner, not pants and sneakers. But most of the time, yup, you have to have the article.
I wouldn't say any of those in English... I will learn the rule in Danish but I don't think it's OK to say it's the same as English.
Yes, you're right of course. I can't think of a consistent rule. To me it sounds wrong to omit the article for some things (e.g. trøje=jersey), but fine for others (e.g. skjorte=shirt) when talking about wearing something.
Hm. Regional differences maybe? To me they all sound right with and without the article (in Danish).
"Jeg har trøje på, så jeg fryser ikke" sounds fine to me.
I can't think right now, but would you use på in other ways? The book is on the table..... ??