Hi Dok,
Thank you very much for your links and the bunch of very useful commands. Overwhelming information actually, part of the super complex (actually overcomplicated) Linux audio model (layers), but I finally could find out what was the problem.
Apparently the Linux system took the mainboard audio output as default (actually highest priority over the HDMI output from the video card). I thought I had corrected that before already but... in the system settings under Multimedia --> Audio and Video Settings (Settings for the Phonon multimedia framework) on the 'Device Preference' tab, not only 'Music' or 'Video' must be changed, also 'Audio Playback' which actually seems to be simply a header for all the other entries (Notifications, Music, Video etc.), whereas actually it's about "Default/Unspecified Category". That's unlogical (at least for my logics
) but so the simple piece of advise is to change all, so there is no doubt about the effect. Concretely Flash Player (Firefox) is considered as "Unspecified Category", meaning it's not touched by the settings of "Music" or "Video". BTW, some media players are having their own audio settings (like SMPlayer) and others (like Dragon Player) are only relying on the system settings. That can also lead to some unexpected / inconsistent results.
Now going through all again I realise that the only way to have it working, in addition to what I wrote above, is to
deactivate the PulseAudio (uncheck the check box in the MCC under Hardware-->Sound Configuration). Doing this, I have a choice of Audio Playback Devices (actually priority, changed through "Prefer"/"Defer" Arrows Up/Down) and so there I can switch between analog audio (mainboard built in) and HDMI (Radeon video card over HDMI). If opposed to this, I leave the PulseAudio check box (see above, MMC) checked (default I guess), then as a result I will have only "PulseAudio Sound Server" as single option left for Audio Playback (and all the sub categories), hence no way at all to switch do the HDMI output !
The "Audio Hardware Setup" tab in the system setting should allow to test the R/L speakers. With my present configuration (no PulseAudio) it's simply not working at all. Regardless it's important to have the desired device (HDMI in my case) in the "Audio Hardware Setup" tab, under Sound Card and under Sound Device. Like this it's now working for me, I have all the audio output signals going to my Radeon video card (HDMI).
I'm not totally satisfied though with this setup, because I would like the audio signal to go the inbuild monitor speakers over HDMI AND at the same time, to have them going to the speaker jack (analog) of the mainboard, which is not working. I can have either the signal going out over HDMI (digital) OR over the speaker jack ouput (PC case front panel, analog) but not both together. To switch I haved to open the system settings and either change the priority on the "Device Preference" tab (see above) or to deactivate the Radeon HDMI on the "Audio Hardware Setup" tab.
I hope all that makes sense. It's a mess between MMC and system settings, like it will probably always be, because of the way all has been built up.