Crystal structure, electronic structure, and magnetic behavior of the spin-1/2 quantum magnet Na1.5VOPO4F0.5 are reported. The disorder of Na atoms leads to a sequence of structural phase transitions revealed by synchrotron x-ray powder diffraction and electron diffraction. The high-temperature second-order α↔β transition at 500 K is of the order-disorder type, whereas the low-temperature β↔γ+γ′ transition around 250 K is of the first order and leads to a phase separation toward the polymorphs with long-range (γ) and short-range (γ′) order of Na. Despite the complex structural changes, the magnetic behavior of Na1.5VOPO4F0.5 probed by magnetic susceptibility, heat capacity, and electron spin resonance measurements is well described by the regular frustrated square lattice model of the high-temperature α-polymorph. The averaged nearest-neighbor and next-nearest-neighbor couplings are J̅ 1≃−3.7 K and J̅ 2≃6.6 K, respectively. Nuclear magnetic resonance further reveals the long-range ordering at TN=2.6 K in low magnetic fields. Although the experimental data are consistent with the simplified square-lattice description, band structure calculations suggest that the ordering of Na atoms introduces a large number of inequivalent exchange couplings that split the square lattice into plaquettes. Additionally, the direct connection between the vanadium polyhedra induces an unusually strong interlayer coupling having effect on the transition entropy and the transition anomaly in the specific heat. Peculiar features of the low-temperature crystal structure and the relation to isostructural materials suggest Na1.5VOPO4F0.5 as a parent compound for the experimental study of tetramerized square lattices as well as frustrated square lattices with different values of spin.