Hello Antoni,
[Topic moved here.]
MIDI files are different to audio files in that they contain events/actions themselves (turning a particular note on or off, or turning a stop on or off, for example), rather than the audio that doing those actions would result in:
Hauptwerk's player plays MIDI files (not audio), which is why you see the keys and stops move when you press the 'play' button (and why you can affect what's playing by altering the registration).
To answer your first question, yes -- you can record a new audio and/or MIDI file (with altered registration) whilst playing an existing MIDI file. See the 'Recording menu | Overdubbing MIDI recording' section in the main Hauptwerk user guide for how to do that (which was on page 136 of the Hauptwerk v4.2.1 version of the guide, given that you're currently using that version).