Conversational AI, such as ChatGPT, is increasingly used for information seeking. However, little is known about how ordinary users actually prompt and how ChatGPT adapts its responses in real-world conversational information seeking (CIS). In this study, a nationally representative sample of 937 U.S. adults engaged in multi-turn CIS with ChatGPT on both controversial and non-controversial topics across science, health, and policy contexts. We analyzed both user prompting strategies and the communication styles of ChatGPT responses. The findings revealed behavioral signals of digital divide: only 19.1% of users employed prompting strategies, and these users were disproportionately more educated and Democrat-leaning. Further, ChatGPT demonstrated contextual adaptation: responses to controversial topics contain more cognitive complexity and more external references than to non-controversial topics. Notably, cognitively complex responses were perceived as less favorable but produced more positive issue-relevant attitudes. This study highlights disparities in user prompting behaviors and shows how user prompts and AI responses together shape information-seeking with conversational AI.