Now I can't get it work. Moreover, when I go to Settings, Reset Settings the mappings do not get cleared. Is this correct behavior? The text in the control app indicates "…reset all… and MIDI settings."
The Reset Settings function in H9 Control resets the app's settings. It doesn't reset the pedal's settings.
But you also described restarting the pedal while holding the right footswitch and the big, black wheel. This should restore the H9 to its factory settings. So, this should clear out any changes you made to the MIDI program change receive map.
For example, I have a USB-midi adapter and a Windows PC. Could someone recommend a simple utility I could use to check my H9's midi connectivity?
Sure, on Windows you can use MIDI Ox to check and make sure that your H9 is actually being sent the MIDI program change messages that you think it's being sent. And you can also use it to send your H9 particular program change messages and check your mappings.
Alternatively, Max MSP can also be used for this, but I wouldn't describe that as a simple utility.