Here, we have studied the crystalline structure of bulk ZnX (X = O, S, Se, Te) and ZnF2 systems as a first step to understand the structures like ZnX and Zn-based systems like ZnO/ZnF2 interfaces, which are of utmost importance for possible technological applications. In addition, an adequate methodological description based on density functional theory (DFT) calculations is necessary. It is well known that plain DFT calculations based on local or semilocal exchange-correlation functionals fail to describe the correct band gap energy for these systems, whereas nonlocal approaches, such as hybrid-based functionals, can compensate the underestimation of band gap. To contribute to the assessment, DFT studies were performed within semilocal Perdew-Burke-Ernzerhof (PBE) and two nonlocal functionals, hybrid Heyd-Scuseria-Ernzerhof (HSE) and PBE + U functionals. Our results confirm that PBE underestimates the energy band gap values, from 33.0 to 42.8% for ZnX compounds compared to the experimental values. Applying the hybrid HSE functional, we obtained a band gap dependency in relation to the range of separation of the nonlocal exact exchange, in general decreasing the band gap error and improving the lattice constant description. In addition, using the PBE + U approach, we have investigated the localization of the Zn d-states and its effect on the band gap in ZnX and ZnF2. We found an increase in the band gap with increasing Hubbard parameter, which introduces on-site Coulomb corrections for the Zn 3d states. In the same context, the relevance to include the Hubbard corrections for the O 2p states (and X p states) is highlighted. Thus, considering PBE + U, the error in ZnO band gap, for example, decreases to 5.1%, in relation to the experimental value. Finally, ZnO-12L/ZnF2-4L superlattices are found to exhibit conventional electronic properties, such as low fundamental band gap, smaller than either of the parent materials. Our first-principles calculations reveal that the unexpected band gap reduction is induced by the conducting layers that tend to penetrate the interface and decrease the band gap, leading to the transport of carriers through the interface to ZnF2, which, even with a high band gap for charge transfer, can be interesting for photovoltaic applications.