This study aims to classify brain tumors in MRI images into four categories: glioma, meningioma, absent, and pituitary tumors, as well as segment low-grade gliomas. We evaluate our proposed models on four publicly available datasets to ensure robustness and generalizability. For classification tasks, we compare the performance of our custom CNN model against established models like ResNet and VGG. For segmentation tasks, we compare our custom U-Net model with the original U-Net and ResNet-based encoders. To validate the effectiveness of our models, we employ the Explainable AI (XAI) method LIME, providing insights into why our custom architectures outperform others. Our custom U-Net model achieves a validation accuracy of 99.79% and an Intersection over Union (IoU) score of 0.889 for low-grade glioma segmentation. Additionally, we report a LIME explanation stability score of 0.8169 and a sparsity score of 0.1190. The proposed custom CNN model achieves a validation accuracy of 98.70%, weighted avg precision of 97.63%, recall of 97.64% and weighted F1 - Score of 97.63%. The model achieves a LIME stability score of 0.923 and a sparsity score of 0.203. These results highlight the potential of our custom models to enhance accuracy and interpretability in brain tumor classification and segmentation tasks, offering significant improvements over existing methodologies. The custom U-net model is also an excellent negative classifier achieving a perfect 1.00 IoU score for classifying MRI scans which do not have any tumor.