The exponential growth of Internet of Things (IoT) devices necessitates fog computing architectures that balance network performance with energy efficiency and environmental sustainability. Traditional fog node placement algorithms decouple energy considerations from optimization processes, leading to excessive grid dependency and substantial carbon emissions. This research introduces Green D-OXA, a novel energy-efficient algorithm for dynamic fog node placement with integrated renewable energy harvesting in sustainable IoT networks. Green D-OXA extends the bio-inspired OX optimizer through four adaptive mechanisms: energy-aware warm-start initialization, adaptive iteration control, intelligent triggering with renewable energy prediction, and explicit solar-wind harvesting models with battery management. The algorithm formulates continuous multi-objective optimization integrating connectivity, coverage, movement costs, energy consumption, renewable utilization, and carbon reduction. Comprehensive experimental evaluation across five dynamic scenarios mobile fog nodes, equipment failures, time-varying traffic, network expansion, and combined dynamics demonstrates superior performance compared to three established baseline algorithms (SPP-TLBO, CSA-FSPP, SPP-DEA). Green D-OXA achieves 97.8% connectivity, 98.4% coverage, 68.5% renewable energy utilization, and 43.4%-56% CO₂ emission reduction. Scalability analysis from 50 to 1000 nodes confirms practical deploy ability with minimal performance degradation and 3.8%-4.9% energy overhead. Results establish Green D-OXA as an effective solution for sustainable large-scale IoT-fog computing infrastructures, advancing green computing initiatives through intelligent renewable energy integration.