I'm not sure stage presence can be worked on. If you just mean skills, yeah, then she can work on stage skills. But many people think stage presence, like talent, is innate. A gift you either have or you don't. I think she has talent, not sure if she has enough stage presence.
It's not about running around, at all, it's about whether she commands the stage. Quiet performers can command the stage. They can sit on a chair and sing (or even just talk), and they have the charisma or "stage presence" to be totally captivating. Kree seems light on this, but maybe it's just me. On the other hand, she made me like her, one way or another, so yeah, maybe she has more than I think.
Yes, I agree there's a difference. Though I think that highlighting one's ability to project sound will generally cause one to be loud.
When she has a song where it works, that's fine. It's similar to Adam when I felt he over-used his "wail" on almost every song. Song interpretation should be about finding the essence of a song and conveying it, as much as possible. This is only my opinion, of course. There's also a school that thinks a song is just something to sing so the audience can hear what you can do with your voice.
In my opinion, singing a song is storytelling and setting a mood, otherwise a singer could just go onstage and sing a lot of wordless notes to show ability to project, or show range, or whatever. Granted there are many ways of interpreting a song and it's okay for two people to differ on the ways they enjoy.
