Pixel-based reconfigurable intelligent surfaces (RISs) employ a novel design to achieve high reflection gain at a lower hardware cost by eliminating the phase shifters used in traditional RIS. However, this design presents challenges for channel estimation and passive beamforming due to its non-separable state response, rendering existing solutions ineffective. To address this, we first approximate the non-separable RIS response functions using a kernel-based method and a deep neural network, achieving high accuracy while reducing computational and memory complexity. Next, we propose a simplified cascaded channel model that focuses on dominated scattering paths with limited unknown parameters, along with customized algorithms to estimate short-term and long-term parameters separately. Finally, we introduce a low-complexity passive beamforming algorithm to configure the discrete RIS state vector, maximizing the achievable rate. Our simulation results demonstrate that the proposed solution significantly outperforms various baselines across a wide SNR range.