Older adult patients constitute a rapidly growing subgroup of Intensive Care Unit (ICU) patients. In these situations, their family caregivers are expected to represent the unconscious patients to access and interpret patients' medical information. However, caregivers currently have to rely on overloaded clinicians for information updates and typically lack the health literacy to understand complex medical information. Our project aims to explore the information needs of caregivers of ICU older adult patients, from which we can propose design opportunities to guide future AI systems. The project begins with formative interviews with 11 caregivers to identify their challenges in accessing and interpreting medical information; From these findings, we then synthesize design requirements and propose an AI system prototype to cope with caregivers' challenges. The system prototype has two key features: a timeline visualization to show the AI extracted and summarized older adult patients' key medical events; and an LLM-based chatbot to provide context-aware informational support. We conclude our paper by reporting on the follow-up user evaluation of the system and discussing future AI-based systems for ICU caregivers of older adults.