Yes, they're all cognate. German teuer, Icelandic dýr, etc. Most if not all modern Germanic languages have it in some form. Although I would say düür in Platt. :)
So "Köttet är dyrt" is "The meat is expensive", but "Det dyra köttet" means "The expensive meat"?
It goes for definite forms as well. All plurals get -a though, regardless of grammatical gender. You'll get the hang of it with time and practice!
This is a quite straightforward translation, where köttet corresponds very precisely with the meat in meaning.
I agree, I know what a definite form is, but what I meant is I'm not sure it's idiomatic to say that in English. I may be wrong though.
Yes, but what I mean to say is that without the article, the sentence is talking about meat in general rather than some specific meat, and both English and Swedish work that way and thus require the definite in translation.