Changing or adding control points

Then what is missing in what you’re trying to do?
You should be free to move the nodes to change the shape of the object.
Note that if you hover over the “Edit Nodes” icon you get additional information about the tool and commands available for node editing.
If you’re looking for how to add/delete/break/etc. nodes that information is available in the tooltip when you hover over the tool. You activate one of the features by hovering over your shape and then pressing the relevant key.