Yes, turns out it takes some effort to be aware of power imbalance and work against it. Those words have different social meanings when spoken to a woman than when spoken to a man.
Yes - people management is kind of like project management in that way. There are lots of things that are obviously wrong to do, but very few things that are always going to work.
I think personally I'd consider it a success just to be aware that whatever you're doing now might not be working, or might not work on this particular person - and with this in mind, look for feedback/signals and adjust your behaviour to circumstances.
That's up to you. Maybe that will become more clear as you see the social power imbalance more clearly. Perhaps your framing of the whole situation would change, I don't know.
There's lots of guidelines about what not to do. There's less guidance about what to do instead.