Graph Neural Networks (GNNs) have shown remarkable success in various graph-based learning tasks. However, recent studies have raised concerns about fairness and privacy issues in GNNs, highlighting the potential for biased or discriminatory outcomes and the vulnerability of sensitive information. This paper presents a comprehensive investigation of fairness and privacy in GNNs, exploring the impact of various fairness-preserving measures on model performance. We conduct experiments across diverse datasets and evaluate the effectiveness of different fairness interventions. Our analysis considers the trade-offs between fairness, privacy, and accuracy, providing insights into the challenges and opportunities in achieving both fair and private graph learning. The results highlight the importance of carefully selecting and combining fairness-preserving measures based on the specific characteristics of the data and the desired fairness objectives. This study contributes to a deeper understanding of the complex interplay between fairness, privacy, and accuracy in GNNs, paving the way for the development of more robust and ethical graph learning models.