Is there one if those box or wire things there, that you can put your carry-on into to make sure it's not too big? I have seen them in other airports.

Yes. Each airline has their own system. Super easy.

It's not super important. I doubt my backpack would actually fit in that thing but I fly all over the country with it. If that run out of room they will have you check the 20" roller kind anyways.

Yes there is

I believe there is