Leveraging grant-free radio access for enabling lowpower wide-area (LPWA) Internet of Things (IoT) connectivity has attracted lots of attention in recent years. Regarding lack of research on LPWA IoT networks, this work is devoted to reliability modeling, battery-lifetime analysis, and operation-control of such networks. We derive the interplay amongst density of the access points, communication bandwidth, volume of traffic from heterogeneous sources, and quality of service (QoS) in communications. The presented analytical framework comprises modeling of interference from heterogeneous sources with correlated deployment locations and time-frequency asynchronous radio-resource usage patterns. The derived expressions represent the operation regions and rates in which, energy and cost resources of devices and the access network, respectively, could be traded to achieve a given level of QoS in communications. For example, our expressions indicate the expected increase in QoS by increasing number of transmitted replicas, transmit power, density of the access points, and communication bandwidth. Our results further shed light on scalability of such networks and figure out the bounds up to which, scaling resources can compensate the increase in traffic volume and QoS demand. Finally, we present an energy-optimized operation control policy for IoT devices. The simulation results confirm tightness of the derived analytical expressions, and indicate usefulness of them in planning and operation control of IoT networks.