Estimation in few-bit MIMO systems is challenging, since the received signals are nonlinearly distorted by the low-resolution ADCs. In this paper, we propose a deep learning framework for channel estimation, data detection, and pilot signal design to address the nonlinearity in such systems. The proposed channel estimation and data detection networks are model-driven and have special structures that take advantage of domain knowledge in the few-bit quantization process. While the first data detection network, B-DetNet, is based on a linearized model obtained from the Bussgang decomposition, the channel estimation network and the second data detection network, FBM-CENet and FBM-DetNet respectively, rely on the original quantized system model. To develop FBM-CENet and FBM-DetNet, the maximum-likelihood channel estimation and data detection problems are reformulated to overcome the indeterminant gradient issue. An important feature of the proposed FBM-CENet structure is that the pilot matrix is integrated into the weight matrices of its channel estimator. Thus, training the proposed FBM-CENet enables a joint optimization of both the channel estimator at the base station and the pilot signal transmitted from the users. Simulation results show significant performance gains in estimation accuracy by the proposed deep learning framework.