Agile maneuvers are essential for robot-enabled complex tasks such as surgical procedures. Prior explorations on surgery autonomy are limited to feasibility study of completing a single task without systematically addressing generic manipulation safety across different tasks. We present an integrated planning and control framework for 6-DoF robotic instruments for pipeline automation of surgical tasks.We leverage the geometry of a robotic instrument and propose the nodal state space (NSS) to represent the robot state in SE(3) space. Each elementary robot motion could be encoded by regulation of the state parameters via a dynamical system. This theoretically ensures that every in-process trajectory is globally feasible and stably reached to an admissible target, and the controller is of closed-form without computing 6-DoF inverse kinematics. Then, to plan the motion steps reliably, we propose an interactive (instant) goal state of the robot that transforms manipulation planning through desired path constraints into a goal-varying manipulation (GVM) problem. We detail how GVM could adaptively and smoothly plan the procedure (could proceed or rewind the process as needed) based on on-the-fly situations under dynamic or disturbed environment. Finally, we extend the above policy to characterize complete pipelines of various surgical tasks. Simulations show that our framework could smoothly solve twisted maneuvers while avoiding collisions. Physical experiments using the da Vinci Research Kit (dVRK) validates the capability of automating individual tasks including tissue debridement, dissection, and wound suturing. The results confirm good task-level consistency and reliability compared to state-of-the-art automation algorithms.