Human-Robot Collaboration (HRC) scenarios demand computationally efficient frameworks that enable natural and safe actions and interactions in shared workspaces. To address this, we propose a novel framework that utilises interactive Gaussian Process (GP) distance fields applying Riemannian Motion Policies (RMP) for key HRC functionality. Unlike traditional Euclidean distance field methods, our framework provides continuous and differentiable distance fields resulting in smooth collision avoidance, efficient updates in dynamic scenes and readily available surface information such as normal vectors and curvature. By leveraging RMPs, our framework supports fast, reactive motion generation, utilising both the distance and gradient fields generated by the GP model. In addition, we propose a Hessian-based normal vector estimation technique that elegantly leverages the GP's second-order derivative information which we utilise for object manipulation. We demonstrate the versatility of our CPU-only system in common HRC scenarios where a collaborative robot (cobot) interacts safely and naturally with a human and performs grasping actions in a dynamic environment. Our framework offers an open-source11https://uts-ri.github.io/IDMP-RMP/, comprehensive and low-computational resource solution for HRC, making it an ideal tool for conducting a wide range of user studies. By providing a continuous and differentiable distance field and combining motion generation, obstacle avoidance, and object manipulation within a single system, we aim to broaden the scope and accessibility of HRC research in real dynamic environments.