Modular manipulators composed of pre-manufactured and interchangeable modules offer high adaptability across diverse tasks. However, their deployment requires generating feasible motions while jointly optimizing morphology and mounted pose under kinematic, dynamic, and physical constraints. Moreover, traditional single-branch designs often extend reach by increasing link length, which can easily violate torque limits at the base joint. To address these challenges, we propose a unified task-driven computational framework that integrates trajectory planning across varying morphologies with the co-optimization of morphology and mounted pose. Within this framework, a hierarchical model predictive control (HMPC) strategy is developed to enable motion planning for both redundant and non-redundant manipulators. For design optimization, the CMA-ES is employed to efficiently explore a hybrid search space consisting of discrete morphology configurations and continuous mounted poses. Meanwhile, a virtual module abstraction is introduced to enable bi-branch morphologies, allowing an auxiliary branch to offload torque from the primary branch and extend the achievable workspace without increasing the capacity of individual joint modules. Extensive simulations and hardware experiments on polishing, drilling, and pick-and-place tasks demonstrate the effectiveness of the proposed framework. The results show that: 1) the framework can generate multiple feasible designs that satisfy kinematic and dynamic constraints while avoiding environmental collisions for given tasks; 2) flexible design objectives, such as maximizing manipulability, minimizing joint effort, or reducing the number of modules, can be achieved by customizing the cost functions; and 3) a bi-branch morphology capable of operating in a large workspace can be realized without requiring more powerful basic modules.