Cohesive zone modelling with zero-thickness interface elements is a widely used framework for simulating crack initiation and propagation in finite element analyses. Despite its effectiveness, the approach is often hindered by high computational costs associated with node duplication and by mesh-dependent crack paths. Adaptive insertion of interface elements has been proposed as a remedy to reduce computational overhead by introducing interfaces only where and when required. However, existing adaptive strategies typically rely on stress-based criteria that are sensitive to mesh configuration, may fail to trigger insertion at the appropriate stage, and can lead to inaccurate traction evaluation due to unfavourable interface elements configurations. In addition, mesh-induced bias in crack path prediction remains a persistent challenge, particularly in three-dimensional settings. This work presents a unified computational framework that achieves efficient and robust adaptive insertion with an enhanced crack path prediction accuracy. The proposed approach enables reliable insertion of interface elements overcoming the numerical shortcomings observed in existing methods, while maintaining computational efficiency. Furthermore, crack propagation is guided by the local traction of interface elements, and the mesh is adaptively reoriented to better align element boundaries with the evolving crack path, thereby reducing mesh dependency. The proposed algorithms improve both the accuracy of traction computation and the fidelity of crack path prediction in two- and three-dimensional problems. Numerical examples demonstrate the effectiveness and efficiency of the proposed approach compared to conventional fracture analysis techniques with interface elements.