In this paper, we investigate an unmanned aerial vehicle (UAV)-assisted edge computing network in a sophisticated three-dimensional (3D) scenario, e.g., a post-disaster urban area with multiple mobile ground terminals (GTs) for resilience. The mission of the UAV is to first collect a set of computation tasks from multiple GT sources, then process them and make joint decisions (computation results) which are finally transmitted to another set of GT destinations. An efficient design is provided aiming at minimizing the total time cost including costs for the task offloading, computations, and decision transmissions, via jointly designing the UAV's trajectory and the scheduling of communications from and to different GTs. In particular, we take into account the practical assumptions on the GTs' mobility, on the obstacle avoidance to 3D buildings, and on that the UAV is possible to fly among buildings, i.e., the flying altitude can be lower than the buildings' heights. To address the established complex and non-convex problem, we first provide a problem transformation by exploiting Markov decision process (MDP), and then propose a deep reinforcement learning (DRL) approach-based solution with a multi-step dueling DDQN (D3QN) method. As a result, an efficient solution is achieved, where the UAV acts as the agent to continuously explore and improve its mobile strategy during interacting with the environment under the proposed method. The simulation results show the advantages of the proposed 3D trajectory design in comparison to a 2D one. In addition, the results confirm the robustness of the proposed design in terms of different GTs' mobility models and UAV flying height/area limits, and illustrate the superiority of unrestricted feasible domains for the UAV flight.