My suggestion

(4.) - One may observe and monitor the MIDI messages received by Organteq in the "Action mapping" tab of the MIDI Mappings window.

(5.) - If I'm not mistaken, an organ keyboard "Set" piston simply saves the current state of the stops to another piston, in order to recall and actuate that combination of stops with one button/piston press. In Organteq, right-clicking a combination-button (virtual piston) and selecting "Snapshot" does the same thing: it saves the current state of the stops to that combination button; then one could right-click the combination button in Organteq, click the MIDI drop-down menu --> Assign MIDI Event, and then push a piston (or some other button) on one's physical MIDI-enabled organ keyboard, to cause that piston to engage or actuate that particular stop-combination in Organteq. One can also insert a new or custom MIDI mapping in the MIDI Mappings window, Action mapping tab, to cause a particular MIDI event (such as a MIDI program change transmitted when pushing a physical piston) to trigger a particular Organteq action (such as activating a particular combination).