Accurately localizing the brain regions that triggers seizures and predicting whether a patient will be seizure-free after surgery are vital for surgical planning and patient management in drug-resistant epilepsy. Stereo-electroencephalography (sEEG) delivers high-fidelity intracranial recordings that enable clinicians to precisely locate epileptogenic networks. However, the clinical identification is subjective and dependent on the expertise of the clinical team. Data driven approaches in this domain are sparse, despite the fact that sEEG offers high temporal-fidelity related to seizure dynamics that can be leveraged using graph structures ideal for imitating brain networks. In this study, we introduce a dual-task graph-neural network (GNN) framework that operates on windowed sEEG recordings to jointly predict seizure-freedom outcomes and identify seizure-onset-zone (SOZ) channels. We assemble non-overlapping 10 second windows from 51 clinical seizures spread across 20 pediatric patients, with sEEG data annotated by clinical experts. For each temporal window we construct a functional connectivity graph via thresholded Pearson correlations and extract rich node features (spectral, statistical, wavelet, Hjorth and local graph features), alongside six global graph descriptors. We optimize a combined cross-entropy loss with a tunable task-weight, and select model hyper-parameters via Optuna. Under window-level 10-fold cross-validation, the model achieves a mean graph-level accuracy of $89.31 \pm 0.0976 \%$ for seizure-freedom prediction and a node-level SOZ localization accuracy of $94.72. \pm 0.0041 \%$. For the best performing model, we ran additive and leave-one-out ablation studies to explore feature importance for graph and node-level accuracy.