Recently, GaN-on-BAs has been synthesized and demonstrated as a promising architecture for efficient thermal management in GaN based high-power electronic devices with remarkably reduced thermal boundary resistance compared to that of GaN-on-diamond. In this paper, we report studies on ideal strengths and band alignments for polar BAs/GaN heterojunctions and superlattices using first-principles calculations. The results show that under normal compression, all BAs/GaN interface configurations show much higher compressive stiffness compared to that in bulk GaN [0001] direction, with the GaN softening during its structural transformation under compression markedly suppressed, which improves protection of the electronic properties under external impacts. The natural band alignments of the mismatched BAs/GaN heterojunctions are calculated by a three-step approach. Most of the heterojunction and all the superlattice interfaces show type-II staggered band offsets. Large polarization built-in electric fields are predicated in superlattice with repeatedly positive- and negative-charged N-As and Ga-B interfaces, producing a saw-tooth like dipole potential, which can effectively separate electrons and holes to different interfaces, desirable for the photocatalytic processes. Our research shows that BAs/GaN heterojunction can not only provide a much-needed alternative to GaN-on-diamond heat dissipation system in future designing of high-power electronic devices, but also offers possibilities of applications in photovoltaic and photocatalytic devices as a type-II semiconductor heterojunction or superlattice.