In this paper, we study a real-time monitoring system in which multiple source nodes are responsible for sending update packets to a common destination node in order to maintain the freshness of information at the destination. Since it may not always be feasible to replace or recharge batteries in all source nodes, we consider that the nodes are powered through wireless energy transfer (WET) by the destination. For this system setup, we investigate the optimal online sampling policy (referred to as the age-optimal policy) that jointly optimizes WET and scheduling of update packet transmissions with the objective of minimizing the long-term average weighted sum of Age-of-Information (AoI) values for different physical processes (observed by the source nodes) at the destination node, referred to as the sum-AoI. To solve this optimization problem, we first model this setup as an average cost Markov decision process (MDP). Due to the extreme curse of dimensionality in the state space of the formulated MDP, classical reinforcement learning algorithms are no longer applicable to our problem. Motivated by this, we propose a deep reinforcement learning (DRL) algorithm that can learn the age-optimal policy in a computationally-efficient manner. We further characterize the structural properties of the age-optimal policy analytically, and demonstrate that it has a threshold-based structure with respect to the AoI values for different processes. We extend our analysis to characterize the structural properties of the policy that maximizes average throughput for our system setup, referred to as the throughput-optimal policy. Afterwards, we analytically demonstrate that the structures of the age-optimal and throughput-optimal policies are different. We also numerically demonstrate these structures as well as the impact of system design parameters on the optimal achievable average weighted sum-AoI.