The objective of the proposed research is to address two major anomaly challenges that occur in modern power systems: (1) fault locating in active distribution systems and (2) detection and identification of false data injection attacks (FDIAs). The growing complexity of distribution networks driven by the growing integration of distributed energy resources (DERs), along with increased cyber vulnerabilities across the power grid, demands robust, real-time solutions for anomaly localization and mitigation. To address the fault locating problem, a novel time-domain algorithm is proposed that utilizes high-fidelity line modeling and Dynamic State Estimation (DSE) to pinpoint the exact fault location and type. This approach overcomes limitations of traditional methods, particularly in scenarios with limited measurements, mixed-phase circuit configurations, and Inverter-Based Resource (IBR)-dominated systems with time-varying fault currents. For FDIA detection and identification, a hybrid framework is proposed that integrates a neural network classifier with DSE. This combination allows for accurate root-cause identification and enables self-healing by replacing compromised measurements with DSE estimated values. Together, these methods will enhance the resilience and reliability of power systems under both physical faults and cyber anomalies.