Future Internet-of-Things (IoT) is expected to wirelessly connect billions of low-complexity devices. For wireless information transfer (WIT) in IoT, high density of IoT devices and their ad hoc communication result in strong interference which acts as a bottleneck on WIT. Furthermore, battery replacement for the massive number of IoT devices is difficult if not infeasible, making wireless energy transfer (WET) desirable. This motivates: (i) the design of full-duplex WIT to reduce latency and enable efficient spectrum utilization, and (ii) the implementation of passive IoT devices using backscatter antennas that enable WET from one device (reader) to another (tag). However, the resultant increase in the density of simultaneous links exacerbates the interference issue. This issue is addressed in this paper by proposing the design of full-duplex backscatter communication (BackCom) networks, where a novel multiple-access scheme based on time-hopping spread-spectrum (TH-SS) is designed to enable both one-way WET and two-way WIT in coexisting backscatter reader-tag links. Comprehensive performance analysis of BackCom networks is presented in this paper, including forward/backward bit-error rates and WET efficiency and outage probabilities, which accounts for energy harvesting at tags, non-coherent and coherent detection at tags and readers, respectively, and the effects of asynchronous transmissions.