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Technically yes, in the same sense that you can use a 4" plate for an 8" steak. A twin box spring is considerably smaller (slightly shorter and much narrower) than a queen mattress. The mattress will stick out nearly a foot on each side of the box spring, and a few inches at either the top or bottom (or both).
No, a twin box spring is not large enough. It would take 2 extra long twin box springs (80 inches in length, as opposed to a regular twin's length of 75 inches), as a kings size mattress is 80 inches long and 76 inches wide (which is twice the width of two twin box springs). Keep in mind that 76x80 is the measurements of an eastern king size mattress, as a western or "California" king mattress measures 72x84 inches.
You could possibly do this, but your box spring will be about 9" too wide and 5" too short. A queen mattress is 60" x 80". A twin regular mattress is 39" x 75". An extra long twin would be 80" long.
If you are referring to something to serve as a foundation/box spring, you need (likely) a Twin bunkie board; which is a 2" version of a box spring. You likely have about 6-7" of space so after the board, you can possibly squeeze a Polypedic twin mattress or the cheaper 4" version. Both sold by Michigan Discount Mattress - just ask for a Twin BUNKIE BOARD ... don't use a piece of plywood like some people will advise you to do. Hope that's helpful.
yes
No.
A box spring.
"Box spring mattresses come in different sizes. There are single, double, queen and king mattress. When you go from a single to a queen or king mattress, the width and length both change. A twin measures at 39x75. A queen measures at 60x80 and a king is 76x80 inches."
Box Spring
yes
A split queen mattress is not as common as a split king sized mattress. A box spring for a queen bed can be purchased when the area for the bed is unreachable by the queen box spring in its original size.
When you are buying a bed there are two pieces. One is the box spring and the other mattress itself. You can use the mattress by itself but to be more comfortable you should get both pieces.