Exotic magnetic orders in two-dimensional (2D) materials are attracting huge interest for energy-efficient spintronic applications, yet realizing robust high-temperature van der Waals antiferromagnets and topological magnetic states remains challenging. In this work, we develop a machine-learning framework for identifying magnetic orders and predicting magnetization using structural, compositional, and electronic information derived from the Materials Project. Fixed-length descriptors are constructed for two complementary tasks: ferromagnetic (FM) versus antiferromagnetic (AFM) classification and quantitative magnetization prediction. Magnetic order is classified using a LightGBM model trained on structure-derived descriptors without explicitly including magnetic descriptors. Five-fold cross-validation grouped by chemical system is used to reduce chemical leakage, together with hyperparameter and classification-threshold optimization. On an isolated test set, the classifier achieves a balanced accuracy of 93.6% in the testing set. Magnetization is predicted using a residual multilayer perceptron with compositional, structural, electronic, and task-specific initial-state descriptors. A logarithmic target transformation and robust weighted loss are used to account for the broad magnetization distribution, while three independently trained models are combined into a final ensemble. The model achieves a mean absolute error of 0.686 μB/formula unit. For selected magnetic candidates, simulated magnetic imaging and phase-reconstruction analysis are further used to investigate magnetization textures and skyrmion-like features through normalized magnetization profiles and topological charge. This framework provides an efficient approach for screening 2D magnetic materials and prioritizing candidates for antiferromagnetic and topological spintronic applications.