High-contrast imaging in the visible and near-infrared (VIS/NIR) has revealed the presence of a plethora of substructures in circumstellar disks (CSDs). One of the most commonly observed substructures are concentric gaps that are often attributed to the presence of embedded forming planets. However, direct detections of these planets are extremely rare, and thus ambiguity regarding the origin of most gap features remains. The aim of this study is to investigate the capabilities of high-contrast VIS/NIR imaging of directly detecting and characterizing low-mass giant planets in gaps in a broad systematic parameter study. To this end, a grid of models of protoplanetary disks was generated. The models include a central T Tauri star surrounded by a face-on CSD harboring an accreting planet, which itself is surrounded by a circumplanetary disk (CPD) and carves a gap. These gaps are modeled using empirically determined profiles, and the whole system is simulated fully self-consistently using the Monte Carlo radiative transfer code Mol3D in order to generate temperature distributions and synthetic observations assuming a generic dust composition consisting of astronomical silicate and graphite. Based on these simulations, we measured the impact the planet and its CPD have on contrast curves and quantified the impact of the observing wavelength and of five key parameters (planetary mass, mass accretion rate, distance to the star, mass of the CPD, and mass of the CSD) on the determined signal strength. Subsequently, we applied a detection criterion on our results and assess the capabilities of the instrument SPHERE/VLT of detecting the embedded planets. We find that a part of the investigated parameter space includes detectable planets, and we elaborate on the implication a non-detection has on the underlying parameters of a potential planet and its CPD. Furthermore, we analyze the potential loss of valuable information that would enable the detection of embedded planets by the use of a coronagraphic mask. However, we find this outcome to be extremely unlikely in the case of SPHERE. Finally, within the VIS/NIR wavelength range we identify for each of the investigated basic properties of the planets and the disks the most promising observing wavelengths that enable us to distinguish between different underlying parameter values. In doing so, we find that the detectability and the characterization often benefit from different observing wavelengths, highlighting the complementarity and importance of multiwavelength observations.