A fundamental objective of the forthcoming sixth-generation wireless networks is to concurrently serve a vast array of devices many of which, such as Internet-of-Things (IoT) sensors, are projected to have low power requirements or even operate in a battery-free manner. To achieve this goal, non-orthogonal multiple access (NOMA) and ambient backscatter communications (AmBC) are regarded as two pivotal and promising technologies. In this work, we present a novel analytical framework for studying the reliability and security of uplink NOMA-based AmBC systems. Specifically, closed-form analytical expressions for both NOMA-users' and IoT backscatter device's (BD's) outage probabilities (OPs) are derived for both cases of perfect and imperfect successive interference cancellation (SIC). In addition, assuming that one NOMA-user transmits an artificial noise in order to enhance system's security, the physical layer security (PLS) of the system is investigated by extracting analytical expressions for NOMA-users' and BD's intercept probabilities (IPs). To gain insightful understandings, an asymptotic analysis is carried out by focusing on the high signal-to-noise (SNR) regime, which reveals that NOMA-users and BDs face outage floors in the high SNR regime as well as that IPs reach constant values at high SNR. Additionally, practical insights regarding how different system parameters affect these OP floors and IP constant values are extracted. Numerical results verify the accuracy of othe developed theoretical framework, offer performance comparisons between the presented NOMA-based AmBC system and a conventional orthogonal multiple access-based AmBC system, and reveal the impact of different system parameters on the reliability and security of NOMA-based AmBC networks.