This paper considers the problem of scheduling uplinks and downlinks transmissions in an Internet of Things (IoT) network that uses a mode-based time structure and Rate Splitting Multiple Access (RSMA). Further, devices employ power splitting to harvest energy and receive data simultaneously from a Hybrid Access Point (HAP). To this end, this paper outlines a Mixed Integer Linear Program (MILP) that can be employed by a HAP to optimize the following quantities over a given time horizon: (i) mode (downlink or uplink) of time slots, (ii) transmit power of each packet, (iii) power splitting ratio of devices, and (iv) decoding order in uplink slots. The MILP yields the optimal number of packet transmissions over a given planning horizon given non-causal channel state information. We also present a learning based approach to determine the mode of each time slot using causal channel state information. The results show that the learning based approach achieves 90% of the optimal number of packet transmissions, and the HAP receives 25% more packets as compared to competing approaches.

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