Suicide is a critical global public health issue, with millions experiencing suicidal ideation (SI) each year. Online spaces enable individuals to express SI and seek peer support. While prior research has revealed the potential of detecting SI using machine learning and natural language analysis, a key limitation is the lack of a theoretical framework to understand the underlying factors affecting high-risk suicidal intent. To bridge this gap, we adopted the Interpersonal Theory of Suicide (IPTS) as an analytic lens to analyze 59,607 posts from Reddit's r/SuicideWatch, categorizing them into SI dimensions (Loneliness, Lack of Reciprocal Love, Self Hate, and Liability) and risk factors (Thwarted Belongingness, Perceived Burdensomeness, and Acquired Capability of Suicide). We found that high-risk SI posts express planning and attempts, methods and tools, and weaknesses and pain. In addition, we also examined the language of supportive responses through psycholinguistic and content analyses to find that individuals respond differently to different stages of Suicidal Ideation (SI) posts. Finally, we explored the role of AI chatbots in providing effective supportive responses to suicidal ideation posts. We found that although AI improved structural coherence, expert evaluations highlight persistent shortcomings in providing dynamic, personalized, and deeply empathetic support. These findings underscore the need for careful reflection and deeper understanding in both the development and consideration of AI-driven interventions for effective mental health support.