Glaciers and numerous glacial lakes that are produced by glacier melting are key indicators of climate change. Often overlooked, supra-glacial lakes develop in the melting area in the low-lying part of a glacier and appear to be highly variable in their size, shape, and location. The lifespan of these lakes is thought to be quite transient, since the lakes may be completely filled by water and burst out within several weeks. Changes in supra-glacial lake outlines and other surface features such as supra-glacial rivers and crevasses on the glaciers are useful indicators for the direct monitoring of glacier changes. Synthetic aperture radar (SAR) is not affected by weather and climate, and is an effective tool for study of glaciated areas. The development of the Chinese GaoFen-3 (GF-3) SAR, which has high spatial and temporal resolution and high-precision observation performance, has made it possible to obtain dynamic information about glaciers in more detail. In this paper, the classical Canny operator, the variational B-spline level-set method, and U-Net-based deep-learning model were applied and compared to extract glacial lake outlines and other surface features using different modes and Chinese GF-3 SAR imagery in the Mount Everest Region of the Himalayas. Particularly, the U-Net-based deep-learning method, which was independent of auxiliary data and had a high degree of automation, was used for the first time in this context. The experimental results showed that the U-Net-based deep-learning model worked best in the segmentation of supra-glacial lakes in terms of accuracy (Precision = 98.45% and Recall = 95.82%) and segmentation efficiency, and was good at detecting small, elongated, and ice-covered supra-glacial lakes. We also found that it was useful for accurately identifying the location of supra-glacial streams and ice crevasses on glaciers, and quantifying their width. Finally, based on the time series of the mapping results, the spatial characteristics and temporal evolution of these features over the glaciers were comprehensively analyzed. Overall, this study presents a novel approach to improve the detection accuracy of glacier elements that could be leveraged for dynamic monitoring in future research.