Performing versatile mobile manipulation actions in human-centered environments requires highly sophisticated software frameworks that are flexible enough to handle special use cases, yet general enough to be applicable across different robotic systems, tasks, and environments. This paper presents a comprehensive memory-centered, affordance-based, and modular uni- and multi-manual grasping and mobile manipulation framework, applicable to complex robot systems with a high number of degrees of freedom such as humanoid robots. By representing mobile manipulation actions through affordances, i.e., interaction possibilities of the robot with its environment, we unify the autonomous manipulation process for known and unknown objects in arbitrary environments. Our framework is integrated and embedded into the memory-centric cognitive architecture of the ARMAR humanoid robot family. This way, robots can not only interact with the physical world but also use common knowledge about objects, and learn and adapt manipulation strategies. We demonstrate the applicability of the framework in real-world experiments, including grasping known and unknown objects, object placing, and semi-autonomous bimanual grasping of objects on two different humanoid robot platforms.