Machine learning has emerged as a promising approach for predicting molecular properties of proteins, as it addresses limitations of experimental and traditional computational methods. Here, we introduce GSnet, a graph neural network (GNN) trained to predict physicochemical and geometric properties including solvation free energies, diffusion constants, and hydrodynamic radii, based on three-dimensional protein structures. By leveraging transfer learning, pre-trained GSnet embeddings were adapted to predict solvent-accessible surface area (SASA) and residue-specific pKavalues, achieving high accuracy and generalizability. Notably, GSnet outperformed existing protein embeddings for SASA prediction, and a locally charge-aware variant, aLCnet, approached the accuracy of simulation-based and empirical methods for pKaprediction. Our GNN framework demonstrated robustness across diverse datasets, including intrinsically disordered peptides, and scalability for high-throughput applications. These results highlight the potential of GNN-based embeddings and transfer learning to advance protein structure analysis, providing a foundation for integrating predictive models into proteome-wide studies and structural biology pipelines.