None of the pad related settings within the TD20 will have any affect on the Zendrum as it sends MIDI data to the TD20, not trigger impulses. The note velocity has already been determined by the time the data arrives at the TD20.
To affect the responsiveness and sensitivity you need to change those settings in the Zendrum itself. The 'noise floor', 'maximum volume' and 'response curve' all work together to determine this "feel". If you are using ZenEdit, you can see these settings graphically on the 'Response/Calibration' screen.
As for the HH pedal, if you are connecting it to the Zendrum then you should probably perform a calibration (details in the Zendrum manual) though you can also use that same screen in ZenEdit to tweak it. The MIDI channel would be the same as the drums (10).
Someone with more experience with external CC pedals and the TD20 can chime in but I'm pretty sure the CC # it uses is #4 (foot control).