Surgical scene Multi-Task Federated Learning (MTFL) is essential for robot-assisted minimally invasive surgery (RAS) but remains underexplored in surgical video understanding due to two key challenges: (1) Tissue Diversity: Local models struggle to adapt to site-specific tissue features, limiting their effectiveness in heterogeneous clinical environments and leading to poor local predictions. (2) Task Diversity: Server-side aggregation, relying solely on gradient-based clustering, often produces suboptimal or incorrect parameter updates due to inter-site task heterogeneity, resulting in inaccurate localization. In light of these two issues, we propose SurgFed, a multi-task federated learning framework, enabling federated learning for surgical scene segmentation and depth estimation across diverse surgical types. SurgFed is powered by two appealing designs, i.e., Language-guided Channel Selection (LCS) and Language-guided Hyper Aggregation (LHA), to address the challenge of fully exploration on corss-site and cross-task. Technically, the LCS is first designed a lightweight personalized channel selection network that enhances site-specific adaptation using pre-defined text inputs, which optimally the local model learn the specific embeddings. We further introduce the LHA that employs a layer-wise cross-attention mechanism with pre-defined text inputs to model task interactions across sites and guide a hypernetwork for personalized parameter updates. Extensive empirical evidence shows that SurgFed yields improvements over the state-of-the-art methods in five public datasets across four surgical types. The code is available at https://anonymous.4open.science/r/SurgFed-070E/.