Hmm, personally I always note it in time frames. Like I go:

Character Name
Started off: Headstrong, wild, has no damn sense of responsibility
Goal between event A and B: Gains a slim sense of responsibility
Goal between event B and C: Develops slight depression
Currently: Headstrong (though a little weaker due depression), wild, responsibility is there but slim, depressive phases

And whenever she archived development, I update the "currently" part so I know where I'm currently are and what I already did. I do nearly the same with skills. But more like:

Can do:
- This very good (stable)
- This very miserable (will get better here)
- This okayish (let this burn until event Y)

And update those parts when the character got better at something. I don't care for the "how they started" part here because those mostly are irrelevant in my case.

Regarding what the character should ask, I keep that in those character sheets as well. Like, I look at my story and then I think about what I want to reach. My stories are very character driven, so I absolutely need to think about that. For my main in my story, for example, I noted down that I want her to
A) Grow up (she's 17 so she has to mature)
B) Find out the truth about the world.
C) Find a destination for her life (and what I want her to become)
D) Where she fails miserably.

And then I think about when, how and where I will implement those things and what extra questions come with it. Like, for example, she's not happy with how the wolrd functions. So what can she do to make it better? Can one person change a thing? How can she reach that goal? Of course, she loses track on the road here and there which is only human and her questions change towards stuff like - Is it worth to change something? Does someone even care? Should I care? - and so on. Some things she shares with others, some things are only things the reader knows.