Can't delete a section of a shape

If I make a circle, and want to delete one quarter of it …
I select the segment I want to delete
and press delete
It goes away, but does not break the shape
(shape remains closed)
If I pres Cut (command-X)
the same thing happens

Is it not possible to cut out a segment of a shape?
I just want to make a three-quarter circle

Likewise, if I may a rectangle
and select two adjacent points
press delete or command-X
it deletes those two points, the segment between them
and the segments not between them
leaving me with two points with a single segment between them

Am I missing something?

Breaking the path with deleting some points is not supported.

What you can do is to first click on a point with the draw tool (or, much faster, add a node to the segment and directly click it again with the draw tool). This breaks the path. If you then select the segment and delete it it should look as intended.