  We show that two uniform lattices of a regular right-angled Fuchsian building
are commensurable, provided the chamber is a polygon with at least six edges.
We show that in an arbitrary Gromov-hyperbolic regular right-angled building
associated to a graph product of finite groups, a uniform lattice is
commensurable with the graph product provided all of its quasiconvex subgroups
are separable. We obtain a similar result for uniform lattices of the Davis
complex of Gromov-hyperbolic two-dimensional Coxeter groups. We also prove that
every extension of a uniform lattice of a CAT(0) square complex by a finite
group is virtually trivial, provided each quasiconvex subgroup of the lattice
is separable.
