World Market has some great platform beds that aren't very expensive. Our king one is from there and we love it.

Yes, you can buy queen box spring that comes in two pieces. We have one and they're very common for this reason. I think they're called a split box spring.

Our box spring doesn't fit up the stairs in our new-to-us house (the stairs curve and the box spring has no give) so our mattress is currently on the floor in our bedroom. I'm assuming we need to buy a platform bed frame. Any suggestions other than IKEA (we will look there, I'm just wondering if there's anywhere else)?

We already have a bedroom set with a headboard, so we really just need something to hold up the mattress.

Alternatively, do they sell 2 box springs that would make up a queen size bed?

TIA!