Ok I found the solution. I write it here to avoid other ones will not receive ANY answer (after have spent money):
The AUDIO MIXER push buttons are related the MUTING and they are NOT of all sources, as one imagine instead
They are related ONLY to the global audio devices in Settings > Audio > Global Audio Devices
IF the audio sources are declared up there, then they show up on the audio mixer panel of OBSwitcher.
Otherwise: "salutamm' a sorret' " ... which in jargon it means: absolutely nothing.
I do hope to have helped somebody else with the same issue.
IMPORTANT: when the tablet under iOS goes in"save screen", the connection is lost. Just restart it.