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Wireless networked control system (WNCS) connecting sensors, controllers, and actuators via wireless communications is a key enabling technology for highly scalable and low-cost deployment of control systems in the Industry 4.0 era. Despite the tight interaction of control and communications in WNCSs, most existing works adopt separative design approaches. This is mainly because the co-design of control-communication policies requires large and hybrid state and action spaces, making the optimal problem mathematically intractable and difficult to be solved effectively by classic algorithms. In this paper, we systematically investigate deep learning (DL)-based estimator-control-scheduler co-design for a model-unknown nonlinear WNCS over wireless fading channels. In particular, we propose a co-design framework with the awareness of the sensor's age-of-information (AoI) states and dynamic channel states. We propose a novel deep reinforcement learning (DRL)-based algorithm for controller and scheduler optimization utilizing both model-free and model-based data. An AoI-based importance sampling algorithm that takes into account the data accuracy is proposed for enhancing learning efficiency. We also develop novel schemes for enhancing the stability of joint training. Extensive experiments demonstrate that the proposed joint training algorithm can effectively solve the estimation-control-scheduling co-design problem in various scenarios and provide significant performance gain compared to separative design and some benchmark policies.