Graph Neural Networks (GNNs) are expressive architectures for learning from complex graph-structured data. However, their practical use is often limited by the high computational cost of neighborhood aggregation. Recent efforts have focused on knowledge distillation from GNNs to inference-efficient Multi-Layer Perceptrons (MLPs). However, most existing works treat this distillation as an embedding alignment problem, overlooking the need to replicate the topology-aware smoothing behavior that arises from message passing in GNNs. Moreover, existing methods are primarily performance driven, ignoring critical real-world requirements such as fairness. In this work, we make two key observations: $\textit{(1)}$ state-of-the-art distillation methods fail to capture the heterogeneous smoothness patterns of GNNs, limiting structural awareness in MLPs, and $\textit{(2)}$ they introduce significant individual and group fairness violations. We introduce $\texttt{FAITH}$, the first $\textit{fair and structurally aware GNN-to-MLP distillation framework with graph-free inference.}$ To improve structural awareness in MLPs, we propose a neighborhood-guided energy alignment objective that transfers not only node-level energy, but also the distribution of energies across local neighborhoods. To improve individual fairness, $\texttt{FAITH}$ introduces a novel $\ell_{2,1}$-norm objective that preserves structured similarity in the learned representations. Additionally, we incorporate a counterfactual invariance objective that explicitly encourages the model to learn representations that are statistically independent of the sensitive attribute. We provide a comprehensive theoretical analysis of $\texttt{FAITH}$, interpreting it through a novel instantiation of the Information Bottleneck principle. Extensive experiments on 11 benchmark datasets show that $\texttt{FAITH}$ achieves stronger structural awareness and delivers a better trade-off between utility and fairness than existing methods.