They look at you funny if you pay by cash in Norway. Don't ask me why I know this.
They're working on a way to make Norway cash-free, so they think you're antiquated.
When I was there, we only paid with a credit card. Even for small amounts and it never seemed odd to any cashier/waiter/employee. Can't even tell you what a kroner looks like...
Is there a difference in acceptance of credit card or debit card? In the Netherlands debit cards a very widely used by credit cards hardly at all.
"Do you want to pay with card?" marked wrong.
In order for that to sound natural in US English, you need an "a" before "card."
Native US English speaker here. I also instinctively put "Do you want to pay with card?"
Native Brit here. We pay with cash or by card (or cash). I've never heard anyone say "pay with card".
Same in Canada.
... by card
... with cash