This work, grounded in differential privacy, addresses practical barriers to adopting privacy-preserving techniques in real-world data analysis. We focus on three key areas: private confidence intervals, heavy hitter detection, and private optimization in interpolation regimes. First, we introduce bootstrap-based algorithms for constructing differentially private confidence intervals, leveraging the Bag of Little Bootstraps (BLB) approach to provide accurate and private confidence sets for various statistics. These methods show strong theoretical guarantees and practical performance on synthetic and real-world datasets. Second, we address differentially private heavy hitter detection in large data domains, crucial for understanding user behavior. Our iterative federated algorithm, optimized for prefix-tree structures, dynamically adapts to user data, reducing costs while maintaining high utility. It features adaptive segmentation, on-device data selection, and deny lists for enhanced performance and privacy. Third, we explore private optimization in the interpolation regime, where solutions minimize all sample losses simultaneously. While general improvements in convergence rates are unattainable, significant speedups are possible for functions with specific growth properties. Our algorithms achieve near-exponentially small excess loss in such cases, advancing the efficiency of private optimization in machine learning. Overall, this thesis enhances the practical implementation of differential privacy, bridging the gap between theoretical guarantees and real-world application, and paving the way for broader adoption and trust in privacy-preserving data practices.