Shadows are a prevalent problem in remote sensing imagery (RSI), degrading visual quality and severely limiting the performance of downstream tasks like object detection and semantic segmentation. Most prior works treat shadow detection and removal as separate, cascaded tasks, which can lead to cumbersome process and error accumulation. Furthermore, many deep learning methods rely on paired shadow and non-shadow images for training, which are often unavailable in practice. To address these challenges, we propose Shadow-Aware and Removal Unified (SARU) Framework , a cohesive two-stage framework. First, its dual-branch detection module (DBCSF-Net) fuses multi-color space and semantic features to generate high-fidelity shadow masks, effectively distinguishing shadows from dark objects. Then, leveraging these masks, a novel, training-free physical algorithm (N$^2$SGSR) restores illumination by transferring properties from adjacent non-shadow regions within the single input image. To facilitate rigorous evaluation and foster future work, we also introduce two new benchmark datasets: the RSI Shadow Detection (RSISD) dataset and the Single-image Shadow Removal Benchmark (SiSRB). Extensive experiments on the AISD and RSISD datasets demonstrate that SARU achieves SOTA shadow detection performance. For shadow removal, our training-free N$^2$SGSR algorithm attains an average processing speed of approximately $1.3$s, which is over $10$ times faster than the SOTA MAOSD while maintains an SRI value close to 0.9 on both the AISD and SiSRB datasets, a level comparable to the advanced RS-GSSR method. By holistically integrating shadow detection and removal to mitigate error propagation and eliminating the dependency on paired training data, SARU establishes a robust, practical framework for real-world RSI analysis. The code and datasets are publicly available at: https://github.com/AeroVILab-AHU/SARU