With many endangered languages at risk of disappearing, efforts to preserve them now rely more than ever on using technology alongside culturally informed teaching strategies. This study examines user behaviors in TALKA, a generative AI-powered chatbot designed for Hakka language engagement, by employing a dual-layered analytical framework grounded in Bloom's Taxonomy of cognitive processes and dialogue act categorization. We analyzed 7,077 user utterances, each carefully annotated according to six cognitive levels and eleven dialogue act types. These included a variety of functions, such as asking for information, requesting translations, making cultural inquiries, and using language creatively. Pragmatic classifications further highlight how different types of dialogue acts--such as feedback, control commands, and social greetings--align with specific cognitive intentions. The results suggest that generative AI chatbots can support language learning in meaningful ways--especially when they are designed with an understanding of how users think and communicate. They may also help learners express themselves more confidently and connect with their cultural identity. The TALKA case provides empirical insights into how AI-mediated dialogue facilitates cognitive development in low-resource language learners, as well as pragmatic negotiation and socio-cultural affiliation. By focusing on AI-assisted language learning, this study offers new insights into how technology can support language preservation and educational practice.