Hello,
It transfers the first image to the PC and the subsequent ones to the camera's card.
That is extremely odd, unless you by "the first shot" you mean a picture that gets taken automatically when the camera is connected.
I assume that after setting the nearest-farthest points, returning to the nearest, and clicking "new stack," HR should move a focus step with each click of "Take Picture"?
No, "Take picture" just takes a shot with the current settings and that's it. If exposure bracketing is configured then "Take shot" will actually shoot a bracketed series, but it does not change focus. What you want to do is simply press "Start shooting" for an automated focus series.
