Social media platforms generate vast, complex graph-structured data, facilitating diverse tasks such as rumor detection, bot identification, and influence modeling. Real-world applications like public opinion monitoring and stock trading -- which have a strong attachment to social media -- demand models that are performant across diverse tasks and datasets. However, most existing solutions are purely data-driven, exhibiting vulnerability to the inherent noise within social media data. Moreover, the reliance on task-specific model design challenges efficient reuse of the same model architecture on different tasks, incurring repetitive engineering efforts. To address these challenges in social media graph analytics, we propose a general representation learning framework that integrates a dual-encoder structure with a kinetic-guided propagation module. In addition to jointly modeling structural and contextual information with two encoders, our framework innovatively captures the information propagation dynamics within social media graphs by integrating principled kinetic knowledge. By deriving a propagation-aware encoder and corresponding optimization objective from a Markov chain-based transmission model, the representation learning pipeline receives a boost in its robustness to noisy data and versatility in diverse tasks. Extensive experiments verify that our approach achieves state-of-the-art performance with a unified architecture on a variety of social media graph mining tasks spanning graph classification, node classification, and link prediction. Besides, our solution exhibits strong zero-shot and few-shot transferability across datasets, demonstrating practicality when handling data-scarce tasks.