Well but then you'd know how I'd use AI to also encompass ML as ways to achieve AI, wouldn't you? It's a subset but not "AI" in the sense of the word. It's part of AI.
No, not really. I've never heard it used in that specific context (meaning excluding "lower" things) without larger explanation that someone is talking about strong AI or AGI or similar. You can define it like that if you want but you'd be railing against decades of academia and now both users and marketing, and deliberately using terms you expect readers to misunderstand.
AI is a broad field covering far simpler techniques like SVMs even if they're not deemed to be as a way to achieve AI.
Rain is water, even if water covers more than rain. Serverless functions still run on servers.