This dissertation explores two pivotal aspects of networked systems operating in increasingly complex and adversarial environments: robust decentralized optimization and privacy preservation. Part I delves into the development of decentralized optimization algorithms, addressing the critical challenge of ensuring system robustness against adversarial threats. It investigates strategies to secure the integrity of consensus and optimization processes in distributed networks, where each node or agent contributes to a global objective without centralized coordination. This exploration underscores the necessity of safeguarding these systems from insider-based data injection attacks, ensuring that collective decision-making remains effective and secure. Through rigorous theoretical analysis and algorithmic design, this part contributes novel methodologies that enhance the resilience and efficiency of decentralized learning frameworks. Part II shifts focus to the imperative of privacy preservation within energy systems, a domain where the collection and analysis of data have become indispensable for operational efficiency and innovation. With the advent of smart grids and distributed energy resources, the volume of sensitive data has surged, raising significant privacy concerns. This section proposes the use of differential privacy (DP) as a mathematically rigorous solution to protect individual data records while allowing for the aggregate analysis necessary for system optimization and planning. By applying DP mechanisms, the dissertation showcases how energy systems can share and utilize data for operational and research purposes without compromising individual privacy or data integrity. This part offers a comprehensive approach to developing privacy-preserving mechanisms, illustrating their application through clustering, synthetic data generation, and anomaly detection, thus facilitating secure and efficient data sharing in the energy sector. Together, these parts provide a holistic view of the challenges and solutions at the intersection of decentralized optimization and privacy preservation in networked systems. The dissertation contributes to the theoretical foundation and practical implementation of robust and privacy-preserving frameworks, offering significant insights for securing and optimizing decentralized systems in adversarial and privacy-sensitive contexts.