I would say that as a student, you would be asking a potential advisor what mix of projects would be an example course of the research. What is "their approach" to the sequence of your grad projects over several years? Examples? What combination of risk/certainty does it have? I think you can tell pretty quickly whether the advisor has this concept even in mind.
Former students should have this idea in their mind too, after finishing the program. If they don't, they haven't learned one of the important things about a PhD...
And if you feel that it's too rude to ask, or the professor can't handle such a question (or you're hesitant to ask) -- either you probably want to find someone who is comfortable with such questions, or better find out why you are uncomfortable. Better to be awkward up front and get the answers you want, than be polite and suffer for 5 years to discover the wrong answer.
I mean, that's a whole nother topic -- this is a huge investment of years of your life. You should ask difficult questions before you make the leap. And the professor should owe you such answers before committing to taking you on.
In fact, it's not that different from an awkward pre-nup contract conversation. Only this time you don't have to be swayed by emotion.
Admittedly approaching this with a non-US perspective, but it seems strange to me that PhD students approach their advisors to see what the project/approach is.
Is it normal (in the US?) for a PhD to be as "guided" or prescribed by the advisor as you suggest above? Perhaps my experience differed, but I went for an advisor who takes an old-fashioned "independent research" focus. That's not to say they were unavailable or disinterested; rather they were there to offer input and guidance when needed, but not to steer or even direct. It was up to me to plan what I wanted to do, when to do it how to go about it, what to write up and publish, which conferences to bother with etc. Perhaps this is unusual, but I felt it was a key part of the experience to deliver your own major research programme.
I'd definitely agree that if you can't ask the questions you outlined above, or if they can't answer it, that is a big red flag. A PhD is about learning to ask questions fundamentally, and then set about answering them, so may as well get started by asking your advisor. I'd also try to get an understanding of the culture of the group and practices, since some research groups have more of a "lab" culture where everyone works as part of a bigger project, while I was involved in the opposite - everyone had their own "thing", but would work together when it was helpful.
Well, my story was 15 years ago and in an area where students were mostly expected to bring their own research questions to the program. I had trouble getting the time of day from potential advisors, to say nothing of interviewing them about potential projects and their advising methodology!
