[raptorjr]

Would it be possible if action Record is given on an already scheduled recording, like in the EPG, or on a running recording, like in LiveTV, that the recording/schedule is cancelled/deleted?

This is the role of the backend to handle duplicate.
Also for addon side, pressing record button will inform the backend to keep the live recording. No more. No recording is scheduled.

I'm just referring to how it works in MythTV frontend. But maybe it is not possible to have the same functionality in Kodi/pvr.mythtv?

If I press Record on LiveTV in MythTV frontend, the recording will move to the Default group, and be saved, but if I press again it will go back to a LiveTV recording group, and be autodeleted when necessary.

And when in the MythTV frontend EPG you only need one button, the Record button, to schedule a recording (and also change type from single to series recording), or cancel with the same button by pressing several times, and go through the alternatives.