My understanding is that many people don't directly ask about caste any more, but they'll actively try to figure it out based on your last name or "innocuous" questions about where you're from, what schools you went to, dietary habits, etc. Is that not so?

I understand it isn't legal to ask about caste in many circumstances. However it isn't hard to guess correctly in most cases, so that doesn't matter.

I'm not from India though, so I'm just repeating what I've heard about a system that makes no sense to me.

Yeah that is all on paper. In practice it is very different