Question $2$

If we swap the definitions of plaquette and vertex operators such that the

plaquette operator is a product of ${}_z$ and the vertex operator is a product of

${}_x,$ do we still get a toric code?

No$,$ because we get a different lattice shape.

No$,$ because in this case plaquette and vertex operators do not commute with

each other.

Yes, because the lattice topology and the Hamiltonian form do not change.

Yes, because it is equivalent to translating all vertices to the adjacent squares.