Does this store carry sturdy backing for framing puzzles

Yes they do! A good selection.

Yes! The foam boards are perfect for puzzles.

Yes

We carry foamcore boards anywhere from 20"x30", up to 40"x60" that can be used for backing. All of which can be cut to the size needed. We also have a thinner option in mat boards, that come in sizes 24"x36", and 32"x40".