I'd like to set the center of an object (let's say its "Center of rotation and skewing") to a specific coordinate.
How can I do that?

Hi.

There are several methods, here are a few;

A.
Select the object,
Use the XML editor (Shift Ctrl X)
set the 'inkscape:transform-center-x and inkscape:transform-center-y values to your desired values
(Remember to click the 'Set' button (or Ctrl Enter by the keyboard) after changing the values.)



B.
Use the guide lines, drag a guideline from the horizontal and vertical rulers,
(double click on the guide line to get a dialog where you can set the exact position)
You can then enable snapping of the rotation center and the guidelines.
Drag the rotation center close to the intersection of the guide lines - it will 'snap' in place.

C.
Enable the grid (Shift #) and snap the rotation center to the grid.

There are more ways (Like snapping to other objects) to achieve this as well.

Good Luck.
RGDS
Ragnar