The integration of terrestrial Internet of Things (IoT) and Non-Terrestrial Networks (NTNs) is a fundamental enabler of ubiquitous connectivity in future sixth-generation (6G) wireless networks. This survey provides a comprehensive assessment of state-of-the-art advancements, key challenges, and emerging industrial applications in IoT-NTN convergence, with a focus on edge intelligence, energy-efficient communication protocols, and direct-to-device (D2D) NTN access. Through a systematic analysis of over 30 seminal studies, we identify critical research gaps in scalability, latency minimization, and interoperability within standardized frameworks. Furthermore, we outline future research trajectories, emphasizing AI-driven network orchestration, quantum-secured NTN links, and dynamic spectrum management to enhance network resilience, security, and spectral efficiency in next-generation NTN-integrated IoT architectures.