Around 30 % of inhabitants of Oslo own a car. The rest rent one when they need to and otherwise do fine without.

But you are focused on the biggest cities. Living there is expensive. I live a while out and commute in several times a week, but walkability and ability to live without a car can vary a lot the further from the bigger cities you get.

Having recently moved back to where I'm from in Norway, I was at first surprised at how much more multi cultured the smaller city has become in the last few decades, so I'd expect you should mostly not need worry, but sadly I can not guarantee you'd never experience being looked at as an outsider. You might experience it more from being a US-ian than from not being blond and blue eyed, though.