Nowadays, III-V semiconductors are interesting candidate materials for the tailoring of two dimensional (2D) graphene-like structures. These new 2D materials have attracted profound interest opening the possibility to find semiconductor materials with unexplored properties. First-principles density functional theory calculations are performed in order to investigate the electronic properties of GaN planar and nanotube morphologies based on Haeckelite structures (containing octagonal and square membered rings). Optimized geometries, band-structures, phonon dispersion, binding energies, transmission electron microscopy images simulations, x-ray diffraction patterns, charge densities, and electronic band gaps are calculated. We demonstrated that GaN Haeckelite structures are stable exhibiting a semiconducting behavior with an indirect band gap. Furthermore, it was found that GaN Haeckelite nanotubes are semiconductor with a band gap nature (direct or indirect) that depends of the nanotube´s chirality and diameter. In addition, it was demonstrated that surface passivation and the interaction with hydrazine, water, ammonia, and carbon monoxide molecules can change the band-gap nature. Our results are compared with the corresponding GaN hexagonal honeycomb structures.