The accelerating aging of the global population has intensified concerns around digital exclusion among older adults, which impedes their access to essential services, social connectivity, and opportunities for lifelong learning. Although generative artificial intelligence (AI) offers promising tools to develop age-friendly digital interfaces, a coherent and practical model for its application in elder education remains underdeveloped. This paper proposes a novel framework termed Generative AI-Driven Adaptive Learning for Seniors (GAIA-Seniors), which integrates personalized content generation, multimodal interaction, and socially assistive AI to address cognitive, sensory, and emotional barriers to technology adoption. We present a mixed-methods study involving 60 older adults in Chengdu, China, combining in-depth qualitative interviews with quantitative surveys to assess the acceptance, usability, and perceived benefit of generative AI-enabled educational tools. The methodology features a purposive sampling strategy, a structured thematic analysis process with inter-coder reliability assurance, and statistical evaluation of engagement metrics. Our findings reveal that AI-driven voice interfaces, adaptive learning pacing, and emotionally responsive tutorials significantly enhance digital literacy and alleviate technology-related anxiety among elderly learners. This study provides evidence-based design principles and an evaluative toolkit for AI applications in aging education, contributing to both academic discourse and practical implementation in smart elderly care.