Using atomistic quantum simulation based on a tight binding model, we investigate the formation of electronic bandgap Eg of graphene nanomesh (GNM) lattices and the transport characteristics of GNM-based electronic devices (single potential barrier structure and p-n junction) including the atomic edge disorder of holes. We find that the sensitivity of Eg to the lattice symmetry (i.e., the lattice orientation and the hole shape) is significantly suppressed in the presence of disorder. In the case of strong disorder, the dependence of Eg on the neck width fits well with the scaling rule observed in experiments [Liang et al., Nano Lett. 10, 2454 (2010)]. Considering the transport characteristics of GNM-based structures, we demonstrate that the use of finite GNM sections in the devices can efficiently improve their electrical performance (i.e., high ON/OFF current ratio, good current saturation, and negative differential conductance behaviors). Additionally, if the length of GNM sections is suitably chosen, the detrimental effects of disorder on transport can be avoided to a large extent. Our study provides a good explanation of the available experimental data on GNM energy gap and should be helpful for further investigations of GNM-based devices.