Yes, yes yes yes and YES
We take SAS frequently both east and west from Stockholm (we usually stop over too to see family as Other Half is a Swede) and just LOVE their premium economy. If you are flying economy then ask at check in the cost of an upgrade, or put in a bid - you may be pleasantly surprised at how cheap it is. You get lounge access, fast track, some really nice food, a great seat and a huge/crisp tv that puts BA to shame. Even down the back in economy it isn't bad - I think they still pass the hot rolls by the basket there too. I don't know, once we took PE we were sold on it and havent sat in economy on SAS since maybe 2009.
Whatever you do, make sure you get a gin and tonic as they serve a fantastic small batch Norwegian gin with proper fever tree tonic. BA is serving Gordon's swill with some Schweppes.
I have transited Copenhagen, but that was many years ago back when I was dating a Dane. Its a super easy airport, extremely clean, and smells like blond wood. Bring cash - its pricey to buy anything, but not nearly as expensive as Oslo. They aren't on the Euro so you will end up with coins in your pocket with holes in them.
Just to note - sometimes people can find Scandis to be too brusque, but if you are from the midwest they are kinda like Minnesotans.