Artificial intelligence (AI) is revolutionizing sectors like financial services, healthcare, and education, driving unprecedented progress and fostering innovation across domains. In this backdrop, basic conversational interface aka chat emerged as the predominant way to interact with AI systems. However, the current Human-AI (H2AI) conversations are fraught with a host of challenges necessitating a critical exploration into their design, strategy, and implications. Human-AI interaction design is hindered by fragmented and disjointed technology-driven approaches that lack design-led strategies to address emotional, adaptive, and holistic aspects of the field. This systematic study addressed this issue by developing conceptual models and frameworks integrating emotional, adaptive, and holistic social dynamics into Human-AI conversation design in professional settings. The comprehensive literature review spanning communication studies, user experience frameworks, design process models and conversational AI technologies revealed four research gaps. Through a multiple case study analysis across various industries, we developed four significant recommendations to enhance Human-AI interaction design. First, a typology of 12 Conversational Archetypes was established, providing a framework to inform dynamic and purpose led conversations in professional settings. Second, the Adaptive Conversational Interaction Dynamics (ACID) framework was introduced, integrating five dimensions—Conversation Management, Expertise and Competence, Emotional Intelligence, Trust and Credibility, and Personalization—to improve user engagement and satisfaction. Third, the Dynamic Experience Design (DxD) process emphasized a symbiotic approach with User Resonant Design principles and to create emotionally resilient and adaptable AI systems. Finally, the Conversational Human-AI Interaction (CHAI) framework integrated interactional, emotional, and ethical dimensions, ensuring AI systems are empathetic and ethically grounded. These contributions offer a comprehensive approach to designing advanced conversational AI that is responsive and adaptive. Further research needs to be undertaken to validate these frameworks through qualitative studies to ensure applicability across wider contexts, scenarios and cultures.