Urban Air Mobility (UAM) has emerged as a promising solution for on-demand aerial transportation in densely populated cities, with the potential to alleviate surface traffic congestion. However, urban airspace presents complex operational challenges, including ultra-high traffic density, elevated air and ground safety risks, and limited supporting infrastructure. These constraints significantly increase the workload of air traffic controllers (ATCo), heightening the likelihood of human error in safety-critical environments. As a result, the realization of UAM operations depends heavily on the development of highly automated traffic management systems. Current air traffic management paradigms are not designed to support large-scale UAM operations in urban environments. Key limitations include the absence of dedicated airspace structures for dense low-altitude traffic, insufficient real-time path planning capabilities under dynamic congestion, inaccurate trajectory prediction caused by irregular surveillance data, and inadequate separation assurance mechanisms for ultra-dense operations. Together, these gaps pose substantial risks to the safety, efficiency, and scalability of future UAM systems. This research proposes an integrated, automation-centric UAM traffic management framework. A corridor-based airspace structure is designed, comprising main and byway corridors that mirror urban traffic flow patterns. A real-time path planning algorithm based on the A* search method is developed to dynamically optimise routes by minimising travel distance and corridor congestion while prioritising main corridors. To address trajectory prediction challenges, a Long Short-Term Memory (LSTM) based model is introduced to handle irregular ADS-B sampling intervals, improving prediction reliability without excessive computational cost. The computational complexity of the proposed algorithms is analysed using Big O evaluation to assess system scalability. Additionally, a seven-layer hierarchical decision-making framework is implemented to provide scalable separation assurance across multiple levels of conflict resolution. Simulation results demonstrate that the proposed framework significantly enhances UAM operational performance. The corridor-based path planning approach achieves improved traffic balance and safety under high-density conditions. The LSTM-based trajectory prediction model improves prediction accuracy by approximately 50% compared to raw ADS-B data and reduces computational time by up to 50% relative to linear interpolation. The hierarchical separation assurance framework reduces loss of separation (LOS) events by up to 90% in ultra-dense traffic scenarios, while maintaining consistent traffic efficiency across varying demand levels. The findings confirm the feasibility and robustness of a highly automated UAM traffic management system capable of supporting safe and efficient operations in complex urban airspace. By integrating novel airspace structures, real-time path planning, accurate trajectory prediction, and multi-layer separation assurance, this research addresses critical infrastructure and automation gaps in UAM. The proposed framework advances the state of the art in safety-critical traffic management and provides a scalable foundation for future research and deployment of UAM and broader unmanned aircraft systems (UAS) in urban environments.