Honestly if a students parent came to me and asked all these questions I'd not answer them in any detail
That's an interesting reaction. For a teacher that wouldn't answer questions by the parent, I wonder if he/she would answer questions from the student. If not, then I know it's not going to work for my kid. Plus, the points I mentioned in the original post is not my own idea. They are a result of collective problem solving and reflections.
...and tell them to see the results of our lessons after a period of time.
What results should we expect? Is it reasonable to expect a breakthrough, or not? As for the "period of time", how long? After two months? Four months? A year? After a period of time, I may be told by the teacher that the kid has many bad habits, that the kid lacks finger strengths, that the kid is not practicing correctly, that's why we don't see much progress. They are valid reasons, aren't they? Or should I view them as red flags? In a nutshell, I chose the path of "trusting the process", doing due diligence at the beginning and then give the teacher more trust and patience to show results.
Do they enjoy the lesson and do you see overall progress?
Do they enjoy the lesson? If the teacher does not have what we are looking for, most likely my kid won't enjoy the lessons, or won't have the motivation to practice / love music. I'm no expert in piano playing, but I do know my kid better than 99% of the teachers. If I know my kid is not going to like it, why do I still put him/her through the suffering?
Otherwise why not teach them yourself if you need every detail?
I'm really confused why you make this statement (yes a rhetorical question is a statement). You sound offended. I didn't mean to offend anyone. I'm simply stating what I'm looking for in a teacher. Out of the five points I raised in the original post, all are "principles" instead of "details". Four are not "piano" specific, but rather plain educational psychology applied in piano teaching. Ensure that the principles align is exactly for the purpose of not having to micromanage!
Now again, there is no perfect teacher. There used to be a "bernhard" in this forum some twenty years ago. If he's around in my neighborhood, I'd sign up with him. But mostly likely I will need to make tradeoffs between these points, and that's okay. I'm only trying to do the necessary due diligence, which I think is what a responsible parent ought to do, not a helicopter parent.