Retrieval-Augmented Generation (RAG) shows significant promise in knowledge-intensive tasks by improving domain specificity, enhancing temporal relevance and reducing hallucinations. However, applying RAG to finance encounters critical challenges: restricted access to proprietary datasets, limited retrieval accuracy, regulatory constraints and sensitive data interpretation. We introduce AstuteRAG-FQA an adaptive RAG framework tailored for Financial Question Answering (FQA), leveraging task-aware prompt engineering to address these challenges. The framework uses a hybrid retrieval strategy integrating both open-source and proprietary financial data whilst maintaining strict security protocols and regulatory compliance. A dynamic prompt framework adapts in real time to query complexity, improving precision and contextual relevance. To systematically address diverse financial queries, we propose a four-tier task classification: explicit factual, implicit factual, interpretable rationale and hidden rationale involving implicit causal reasoning. For each category, we identify key challenges, datasets and optimisation techniques within the retrieval and generation process. The framework incorporates multi-layered security mechanisms including differential privacy, data anonymisation and role-based access controls to protect sensitive financial information. Additionally, AstuteRAG-FQA implements real-time compliance monitoring through automated regulatory validation systems that verify responses against industry standards and legal obligations. We evaluate three data integration techniques — contextual embedding, small model augmentation and targeted fine-tuning — analysing their efficiency and feasibility across varied financial environments. Our experimental results show that the framework improves response accuracy by 23% and enhances regulatory compliance by 18%, compared to the baseline systems. Furthermore, qualitative case studies illustrate the robustness of the system in handling complex financial queries whilst maintaining transparency and preserving confidentiality. This study presents a scalable, secure and domain-adaptive solution for sensitive and regulated financial environments.