2009/7/22 Dan Muresan <danmbox@gmail.com>
Is there a way to insert a rest in the middle of a segment, and have the
subsequent notes "shift to the right"? Currently, entering a rest in the
middle of the segment seems to overwrite a range of notes (with silence).

One way I know is to select the notes first and then drag them right (click and hold).
A rest is inserted automatically.

Similarly, is there a way to change a note's duration, and have
subsequent notes shift to the right?

In notation editor, menu  Adjust->Rescale->Double Durations?